
Class JA i^o 
Book____B3^ 
Copyright^" 

COPYRIGHT DEPOSIT. 



WORKS OF 
AUSTIN T. BYRNE, C. E., 



PUBLISHED BY 



JOHN WILEY & SONS. 



Inspection of the Materials and Workmanship 
Employed in Construction. 

A reference book for the use of inspectors, super- 
intendents, and others engaged in the construction 
of public and private works. i2mo, cloth, 555 pp., 
$3.00. 

A Treatise on Highway Construction. 

Designed as a text-book and work of reference 
for all who may be engaged in the location, 
construction, or maintenance of roads, streets, 
and pavements. 8vo, cloth, 936 pp., %.oo. 



INSPECTION 

OF THE 

Mateeials and Wokkmanship 

EMPLOYED IN 

CONSTRUCTION. 

A Reference Booh for the Use of Inspectors^ Superin- 
tendents, and Others Engaged in the Construe^ 
tion of PuHic and Private Works, 

CONTAINING 

A COLLECTION OF MEMORANDA PERTAINING TO THE DUTY OP 

INSPECTORS; QUALITY AND DEFECTS OF MATERIALS; 

REQUISITES FOR GOOD CONSTRUCTION; METHODS 

OF SLIGHTING WORK; 

ETC., ETC. 



BY 

AUSTIN T. BYRNE, 

Civil Engineer, 
Author of *' Highway Construction,''^ 



SECOND edition; revised and enlarged 

FIRST THOUSAND. 



I^EW YORK! 

JOHN WILEY & SONS. 

London: CHAPMAN & HALL. Limited. 

1902. 




^ 



THE LIBRARY OF 

COHGRES8» 
Two Copies Reccived 

SEP. iy 1902 

nCOPVWOWT EWTRV 

0LAS9 ^^-XXa No. 

^ ^ Ll^S 
COFV B. 



T/\]Jo 



Copyright, 1898, 1902, 

BY 

AUSTIN T. BYRNE. 



* • • • •• 
'• I • • 






ROBERT DRUMMOND. PRINTER. NEW YORK. 



^- 



PREFACE TO THE SECOND EDITION. 



In preparing the second edition of the Pocket-book for the 
press, I have taken advantage to import various new matters 
into the text, and, at the same time, to revise or alter the text 
where it has been found necessary. 

I wish to advise my readers that I am open to hints or sugges- 
tions with a view to improve or perfect the contents of this book, 
and that I shall receive them with pleasure. 

A. T. Byrne. 



PREFACE. 



During a long acquaintance with inspectors on public and 
private works I have been frequently asked to recommend a 
concise manual defining the duties of inspectors and describing 
the characteristics of the materials employed, the methods of 
preparing them, and the manner in which work is slighted ; but 
I have felt myself unable to make a satisfactory selection, 
chiefly for the reason that the desired information is contained 
in the text-books of civil engineering and architecture mixed 
with scientific discussions that are of but little interest to an^ 
but the engineer or architect. 

Therefore I have set myself the task of selecting and adapt- 
ing the desired matter to the wants of inspectors and others 
engaged in supervising the construction of civil works. 

The aim of this publication is to present in as concise a form 
as possible (1) the duties of the inspector; (2) the character- 
istics and defects of the materials used in construction; (3) a 
description of the methods employed in preparing the materials 
for use; (4) the manner of placing the prepared materials in 
the structure; and (5) to indicate the points to which the in- 
spector must direct his especial attention to secure a faithful 
compliance with the plans and specifications. 

While presenting the generally approved methods of prepar- 
ing materials, etc., it must he distinctly understood fhat the 
directions or suggestions set forth are not intended to run 
counter to, or he employed in opposition to, the directions and 
instructions given in the specifications under which the work is 
heing prosecuted, 

Reference to authorities has not usually been given in tlie 
text; instead, a list of the various text-books and technical 
dictionaries consulted is given at the end of the book. To the 
authors of these works the writer desires to give his thanks and 
acknowledge his indebtedness for information and suggestions. 



TABLE OF CONTENTS. 



CHAPTER I. 
DUTIES OF INSPECTORS. 

PAGE 

Inspection of the Materials to be employed — Inspection of the 
Methods used in Preparing the Materials — ^Inspection of the Con- 
struction or Placing of the Materials in the Structure — Marking 
Rejected Material — Removal of Rejected Material — Right to require 
Special Methods of Manufacture — Necessity of Constant Vigilance — 
Removal of Incompetent Workmen — Interpretation of Specifica- 
tions — Diary — Records — Reports — Failure to comply with Speci- 
fications — Complaints, how made — Arguments and Disputes — Ad- 
justment of Disagreements 1-3 



CHAPTER II. 
STRUCTURAL MATERIALS. 

Sec. I. Natural Stones. 

Classification of Stones: 

Geological Classification 4 

Physical Classification 4 

Chemical Classification 5 

Requisites for Good Building Stone: 

Durability 5 

Strength 6 

Cheapness 6 

Appearance 6 

Tests for Stone: 

Porosity or Absorption 6 

Effect of Frost 6 

Effect of the Atmosphere 7 

Preservation of Stone 7 

Sec. TT. Description of Building Stones. 
Silicious Stones: 

Granite— Syenite— Cineiss— Mica-slate— Trap— Sandstones S-lO 

Argillaceous Stones: 

Slate— Clay-slate 11 

V 



VI TABLE OF COKTEHTS. 

PAQK 

Calcareous Stones: 

Limestones — Marble 11-12 

Inspection of Stone: 

Appearance of Fracture — Defects of Granite — Sandstone and Lime- 
stone — Test for Soundness — Quarrying — Seasoning 16-17 

Sec. III. Artificial Stones. 

Brick: 

Clay— Manufacture of Brick— Color of Brick— Classification of Brick 
— Rank of Bricks— Glazed and Enamelled Bricks— Size and Weight of 
Bricks 18-23 

Inspection of Brick: 

Soundness, Hardness, Shape, and Size — Strength — Porosity — Effect 

of Frost 24-25 

Fire-brick : 

Fire-clay— Quality— Size 25-26 

Terra-cotta : 

Manufacture — Shrinkage — Color — Quality — Strength — Porous Terra- 
cotta 26-28 

Tiles: 

Common Tiles— Encaustic Tiles— Paving Tiles— Roofing Tiles— Flat 
Tiles— Pan Tiles— Inspection of Tiles 28 

Stones made by Patented Processes 29 

Sec. IV. Cementing Materials. 

Limes : 

Rich Lime — Poor Lime — Hydraulic Lime — Quality of Lime — Preser- 
vation of Lime — Slaking Lime .30-32 

Memoranda and Definitions of Lime: 

Market Form— Weight 3.S 

Portland Cement: 

Definition — Qualitj^ — Color — Fineness — Weight — Specific Gravity — 
Tensile Strength — Setting — Expansion and Contraction — Overlimed — 
Blowing and Swelling 34-85 

Natural Cements: 

Rosendale — Definitions — Characteristics — Color — Weight — Specific 
Gravity— Tensile Strength 35-36 

Inspection of Cement: 

Sampling — Labelling — Marking Rejected — Adulteration of Portland 
Cement— Tests for Cement — Setting— Expansion— Soundness— Ball Test 
— Preservation of Cement 36-38 

Cement Memoranda and Definitions: 

Market Form — Weight — Activity — B'incness — Freezing of Cement Mor- 
tar— Hydraulicity — Hydraulic Activity— Hydraulic Energy— Quick- 
and Slow-setting — Strength — Setting — Soundness 38-41 

Miscellaneous Cements : 

Slag Cement — Description— Tests — Pozzuolanas— Roman Cement— 
Lafarge Cement 42-43 

Asphaltum : 

Description — Characteristics — Asphaltic Cement 43-54 



TABLE OF CONTENTS. ' Vll 



Sec. V. Timber. 

PAGK 

Structure of Timber: 

Properties of Timber — Weight and Strength , . 55-61 

Seasoning Timber: 

Natural Seasoning— Water Seasoning— Artificial Seasoning 62 

Shrinkage and Expansion of Timber: 

Shrinkage of Different Woods — Expansion by Water — Expansion by 
Heat. .... 63-64 

Durability and Decay of Timber: 

Dry Rot— Detection of Dry Rot— Wet Rot— Common Rot— Worms. 64-65 

Processes for Preserving Timber: 

Burnett's— Wellshouse's—Thilmany's—Kyan's—Creosoting— Payne's 
— Seeley 's — Vulcanizing 66-68 

Inspection of Treated Timber: 

Testing Timber treated with Zinc Chloride— Form of Report 69-71 

/Measurement of Timber 73 

Inspection of Timber: 

Appearance of Good Timber — Defects of Timber — Amount of Moist- 
ure in Timber 73-75 

j3^eneral Rules for Classifying Lumber: 

Recognized Defects — Imperfect Manufacture — Standard Lengths.. 76-77 

Rules for Grading Finished Lumber: 

Grades— First and Second Clear Finish — Third Clear Finish— Edge- 
grain Flooring— Flat-grain Flooring— Common Flooring — Ceiling — 
Bevel and Drop Siding— Partition— Moulded Casings and Base 78-80 

Rules for Grading Common Boards and Rough Lumber : 

Cbmmon Boards— Fencing— Dimension— Dressed Timber— Rough 
Yellow Pine — Flooring and Finishing — Common Boards— Rough 
Timber , , 81-82 

Standard Dimensions of the Southern Lumber Manufacturers' Associa- 
tion : 
Flooring— Ceiling— Finishing Boards— Fencing— Dimension 83 

Inspection of Yellow-pine Lumber 83-86 

Inspection of White Pine, Spruce, etc 87 

Hardwood Lumber Grades 87 

Quartered Oak, Pine, etc •«.••••• ..... 8' 



Sec. VI. Metals. 

Iron J 
Pig Iron— Composition— Impurities in Pig Iron and Their Effect- 
Materials produced from Pig Iron 90-93 

Cast Iron : 

Varieties of Cast Iron 94 

Properties of Cast Iron : * 

Weight— Strength— Expansion and Contraction .., c... 95-96 

Notes on Founding : 

Casting with a Head— Pipe and Column Casting 97 

Inspection of Cast Iron 98 

Malleable Cast Iron 100 

Inspection of Malleable Cast Iron 100 



Vin TABLE 0^ CO:N^TE]SrTS. 

PAOB 

Wrought Iron : 

Refining— Puddling— Shingling— Rolling— Composition of Wrought 
Iron 101-102 

Properties of Wrought Iron : 

Weight— Strength— Expansion by Heat— Contraction— Strength of 
Welds— Tenacity at High Temperatures 102-10.^ 

Mill Inspection of Wrought Iron : 

Appearance of Fracture — Defects of Iron 104 

Tests for Wrought Iron 105 

Steel: 

Definition— Characteristics— Varieties— Blister Steel— Sheai Steel — 
Puddled Steel — Bessemer Process— Basic Process— Open-hearth 
Process— Siemens Martin Process— Acid and Basic— Bessemer and 
Open Hearth— Cast Steel 109-111 

Classification of Steeh 

Mild— Soft— Medium— Hard— Tank— Shell— Flange— Fire-box. ... 111-112 

Properties of Steel: 

Specific Gravity — Weight— Expansion and Contraction — Strength- 
Tenacity at High Temperatures— Strength of Welds 112-114 

Steel Alloys: 

Manganese, Nickel, Chrome, and Tungsten Steels— Compressed 
Steel 114-115 

Terms used in Steel- working , 115-116 

Mill Inspection of Steel: 

Steel Ingots : Defects— Appearance of Good Steel— Marking Ingots- 
Melt Records. Rolled Steel : Defects— Appearance of Fractured 
Surface— Steel for Boilers -S^eeZ Castings : Defects — Appearance of 
Fracture— Shrinkage — Specifications 117-121 

Tests for Steel . . 122-124 

Shop Inspection of Iron and Steel 125-128 

Notes on Working Iron and Steel: 

Cold-rolling- Punching and Shearing— Annealing— Forging— Weld- 
ing — Hardening — Tempering — Upsetting — Calking — Blue-short- 
ness 129-131 

Copper: 

Characteristics— Properties— Use— Tests— Weight 132-133 

Lead: 

Characteristics— Properties— Use— Weight 134-135 

Tin: 

Characteristics— Properties— Tin Plate— Tin Roofing-plates 136-140 

Zinc: 

Characteristics— Properties — Use 141 

Alloys: 

Brass— Bronze— Aluminum Bronze— Phosphor Bronze— Manganese 
Bronze 142 

Solders : 

Composition— Soldering— Fluxes for Soldering 144 

Tests for Materials 145 

Testing Strength of Materials : 

Tensile Tests— Examination of Machine— Speed— Specimens— Ten- 
sion— Compression— Transrerse Impact or Drop Tests 146-14S 



TABLE OF CONTENTS. IX 

PAGE 

CoDtraction or Shrinkage of Metals : 

To Compute Weight of Cast Metals by Weight of Pattern 148-149 

Sec. VII. Miscellaneous Materials. 

Sand: 

Description — Silicious— Argillaceous—Calcareous— Pit-sand -River- 
sand— Sea-sand— Use of Sand— Fineness of Sand— Weight— Testing 

; Cleanness— Sharpness— Presence of Salt— Clay— Preparation of 
Sand— Screening— Washing— Drying 150-158 

Gravel: 

Description— Use— Preparation— Weight 152 

Clay: 

Description— Varieties 153 

Gypsum: 

Plaster of Paris— Description— Use 154 

Mineral Wool: 

Description — Use — Weight 154-155 

Asbestos: 

Description — Varieties 156 

Tar: 

Coal-tar— Paving pitch— Wood- tar 156 

Creosote: 

Description— Requisites for Preserving Wood— Wood Creosote— 
Fernoline 157 

Sheathing Felt and Papers 158 

Glue , 159 

Rope: 

Materials employed— Quality of Hemp— Adulterations of Hemp- 
Tests— Strength 160-161 

Wire: 

Gauges— Weight and Strength 162-167 

Wire Rope: 

Manufacture— Varieties— Size— Strength 168-172 

Sec. VIII. Fastenings. 

Nails: 

Cast Nails— Wrought Nails— Cut Nails— Wire Nails— Copper— Com- 
position— Holding Power of Nails— Length of Nails 174-175 

Screws: 

Variety — Dimensions — Lag Screws — Holding Power of Screws — 
Screws for Metal 180-182 

Pins— Treenails—Wedges and Keys. 182 

Bolts and Nuts: 

Varieties — Drift-bolts— Nuts— Inspection— Standard Dimensions- 
Weight -Strength— Washers 183-184 

Rivets: 

Description— Size— Length — Form — Button— Cup — Hammered — 
Countersunk— Pitch— Styles of Riveting— Weight of Rivets— Field- ■ 
rivets — Conventional Rivet-signs — Riveting— Hand-riveting— Mach- 
ine-riveting— Calking— Cold-riveting 188 



X TABLE OF CONTEI^TS. 

PAGE 

Inspection of Riveting: 

Test for Rivet-metal — Essentials of Good Riveting — Heating 
Rivets— Loose Rivets —Marking Rivets to be Cut Out 194 

CHAPTER HI. 
CONSTRUCTION. 

Sec. I. Earthwork. 

Definition: 

Classification— Prosecution of Earthwork— Duty of Inspector- 
Slopes of Earthwork— Increase and Shrinkage of Excavated Ma- 
terial 198-200 

Excavation: 

Loosening— Removing— Amount Moved— Length of Haul— Capac- 
ity of Vehicles 201-202 

Rock Excavation: 

Drilling— Hand-drilling — Machine-drilling— Blasting — Explosives. 203-205 

Precautions to be observed in Blasting 206 

Dredging: 

Types of Dredges— Removing Dredged Material— Marking Area- 
Duty of Inspector 207 

Embankments: 

Methods employed in Constructing „ 208 

Sec. II. Foundations. 

Definitions: 

Object— Duty of Inspector 209 

Natural Foundations: 

Rock— Sand— Clay— Bearing Power of Soils— Loads on Founda- 
tions 210-211 

Artificial Foundations : 

Caissons — Vacuum Process— Plenum Process — Coffer-dams — Cribs 
—Freezing Process— Grillage — Piles 211-214 

Description of Piles 215-217 

Pile-driving: 

Pile-driving Machines— Water-jet— Splicing Piles 218-221 

Inspection of Piles 221 

Clay Puddle: 

Quality of Clay— Tests— Puddling 22^223 

Concrete: 

Essentials of—Materials— Strength— Weight— Proportions of Materi- 
als— Mixing— Inspection— Laying— Depositing under Water— Lait- 
ance— Asphaltic Concrete 224-229 

Sec. III. Masonry. 

Classification of Masonry 230 

Preparation of the Stones: 

Classification of the Stones 230-23J 

Stone-cutting: 

Dressing Granite— Sandstone— Limestone— Marble— Slate 231-236 

Methods of Finishing the Faces of Cut Stone: 

Rough-pointed — Fine-pointed— Crandalled — Axed — Bush -hammered 

—Rubbed— Diamond Panels 237-23P 



TABLE OF CONTENTS. Xl^ 

PAGE 

Tools used in Stone-cutting 238-240 

Definitions of the Terms used in Stone-cutting, 240-241 

Inspection of Cut Stone 241-242 

Mortar: 

Mixing— Measuring Materials— Amount of Cement and Sand re- 
quired for One Cubic Yard of Mortar— Quality of Sand— Water— Re- 
tempering Mortar — Freezing of Mortar 243-248 

Ashlar Masonry: 

Size of Stones— Thickness of Mortar-joint— Bond— Amount of 
Mortar 248-249 

Squared-stone Masonry « 250 

Broken-ashlar Masonry 250 

Rubble Masonry: 

Uncoursed— Coursed— Inspection , 251-252 

Ashlar Backed with Rubble 253 

General Rules to be observed in Laying All Classes of Stone Masonry. . 253 

Brick Masonry : 

General Rules to be observed in Building with Bricks — Wetting 
Bricks — Laying— Amount of Mortar— Pressed-brick Work — Brick 
Masonry Impervious to Water — Efflorescence 254-258 

Repair of Masonry 258 

Definitions of Terms used in Masonry: 

Bond— Coping— Course— Footing— Grout— Header— Joints— Lintels- 
Pointing— Rip-rap— Stretcher— Walls — Thickness of Walls — Safe 
Working Loads for Masonry 259-273 

Description of Arches 274-275 

Definitions of Parts of Arches 275-276 

Construction of Arches: 

Centring for Arches— Striking the Centre ♦ 276-378 



Sec. IV. Carpentry. 

Inspection of Carpentry 279 

Joints: 

Methods of Forming— Fishing— Lapping— Scarfing— Halving— Dove- 
tail— Notching— Mortise and Tenon 280-281 

Flooring: 

Single — Double — Hardwood — Parts of Floors — Bridging — Trim- 
ming 282-285 

Roofs: 

Framing— Parts of Roofs 286 

Stairs: 

Construction— Parts of Stairs 287-288 

Doors: 

Framing— Parts of Doors. . 289 

Standing Trim: 

Architraves — Base-board— Linings — Mouldings — Wainscoting 290-291 

Windows: 

Construction— Setting. 292 

yerins used in Carpentry v JJ93 'J9T 



Xll TABLE OF CONTENTS. 

Sec. V. Iron and Steel, Work, 

Erection of Iron and Steel Structures: 

Column-bearings— Bed- and Cap-plates— Setting Beams Parallel- 
Setting and Connecting Beams — Beam-connections — Anchoring 
Beams— Lintels and Girders 298-301 

Fire-proof Floors: 

Brick Arches— Hollow Tile— Laying Tile— Strength of Tile Arches 
—Tests for Tile Floors— Concrete Floors aOl-Sa 

Sec. VI. Roofing. 

Inspection of Roofing: 

Tin— Tiles— Shingles— Slates— Galvanized Iron— Copper— Weight of 
Roof-coverings 307-314 

Flashing— Counter— Cap— Gutters— Valleys 315-31^ 

Sec. VII. Plumbing. 
Inspection of Plumbing: 

Lead Pipes— Cast-iron Soil-pipes— Water Test— Peppermint Test- 
Smoke Test 317-322 

Sec. VIII. Plastering. 

Definition of Plastering 328 

Materials and Terms used in Plastering : 

Brown Coat— Coarse Stuff— Fine Stuff— Finishing Coat— Gauge Stuff 
Grounds — Hair— Laths— Lime Mortar— Plaster of Paris— Sand— 
Scratch-coat— Stucco— Two-coat Work— Three-coat Work 324-33? 

/Tools used in Plastering 333-339 

Inspection of Plastering 336-337 

Sec. IX. Glass and Glazing. 
Glass: 

Defects— Varieties— Thickness and Weight 338 

Glazing 339 

Sec. X. Painting. 

Materials employed for Paint : 

Bases— Vehicles— Solvents— Stainers—Driers— Properties of Ingre- 
dients 340-346 

Special Paints 346-347 

Varnish 348-349 

Miscellaneous: 

Japanning— Staining — Whitewash— Kalsomine 350 

Inspection of Painting , 351-353 

Sec XI. Water-supply. 

Materials employed 354 

Inspection of Cast-iron Pipe: 

Testing Quality of Metal— Coating the Pipes— Hydraulic Proof— Lay- 
ing the Pipe— Calking— Testing the Pipes— Back Filling— Dimen- 
sions and Weight of Cast-iron Pipe— Weight of Standard Specials — 
Weight of Lead and Gasket per Joint 354-863 

Inspection of Steel Pipe 368-365 

Inspection of Valves and Hydrants 865 



TABLE OF CONTENTS. XIU 

Sec. ZII. Sewerage. 

PAGE 

Materials employed for Sewers: 

Vitrified Pipe— Inspection of Pipe— Testing— Manholes— Lamp-holes 
—Hush Tanks 866-368 

Inspection of Sewer Construction : 

Pipe Sewers— Brick Sewers 36S-369 

Sec. XIII. Paving. 

Materials employed for Paving 371 

Granite-block Paving: 

Manufacture of Blocks 371 

Inspection of Granite-block Paving 372 

Paving-pitch 373 

Wood Pavements 374 

Asphalt Pavements 374-382 

Broken-stone Pavements: 

Telford— Macadam 383-384 

Brick Pavements 385-386 

Artificial-stone Pavements 387 

Flagging 388 

Curbstones 388 

Chapter IV. Miscellaneous. 

Weights and Measures 389-394 

Specific Gravity and Weight of Materials , 395 

Mensuration 408 

of Surfaces— Polygons— Solids— Properties of the Circle 410 

of Areas and Circumference of Circles 411 

Trigonometrical Functions , 461 

Definition of Terms used in Construction 499 



LIST OF TABLES. 



NO. PAGE 

1. Absorptive Power of Stones 6 

2. Specific Gravity, Weight, and Resistance to Crushing of Stones 13 

3. Size and Weight of Brick 23 

4. Specific Gravity and Resistance to Crushing of Brick. 23 

5. Resistance to Crushing of Terra-cotta » 27 

6. Strength of Cement Mortar 42 

7. Description and Properties of Timber 56 

7a. Board Measure 72 

8. Composition of Pig Iron 91 

9. Elongation and Elasticity of Cast Iron 96 

iO. Weight of Cast-iron Plates, Round and Square Bars 99 

11. Composition of Wrought Iron 102 

12. Weight of Flat-bar Iron 106 

13. Weight of Iron and Steel Plates, Round and Square Bars 108 

14. Physical Properties of Open-hearth Basic Steel 113 

15. Weight of Round Copper 132 

16. Weight of Copper and Brass Sheets and Wire 133 

17. Thickness and Weight of Sheet Lead 135 

18. Size and Weight of Tin Plate 139 

19. Weight of Sheets of Wrought Iron and Steel 140 

20- Composition of Alloys 143 

21. Composition of Solders 144 

22. Size of Sieves for Sifting Sand 151 

S3. Coefficients for Computing Strength of Ropes 161 

24. Strength of Manila Rope 162 

25. Wire and Sheet-metal Gauges , 163 

26. U. S. Standard Gauge for Sheet and Plate Iron and Steel 164 

27. Weight of Iron, Steel, and Copper Wire 165 

28. Size and Weight of Iron and Steel Wire 166 

29. Tensile Strength of Wire » 167 

30. Number of Yards of Iron Wire to the Bundle 167 

31. Strength of Iron Ropes 169 

32. Strength of Steel Ropes 170 

33. Strength of Galvanized Wire Rope . . o . . . 171 

34. Strength of Flat Wire Rope 171 

35. Strength of Galvanized Steel Cables „ . 172 

36. Strain on Hoisting Chains and Cables 172 

37. Strength of Cable Chains 173 

38. Wrought-iron or Clinch Nails, Length and Number to the Pound. . .„ 175 

XV 



XVl ; LIST OF TABLES. 



PAGE 

i9. Cut Nails, Length and Number to the Pound 176 

40. Tacks, Size and Number per Pound , 176 

41. Wire Nails, Length and Number to the Pound 177 

42. Wrought Spikes, Size and Number to the Pound 178 

43. Wire Spikes, Size and Number to the Pound 178 

4^. Track Spikes, ^ze and Number per Keg 179 

4b. Street-railway Spikes, Size and Number per Keg 179 

40. Dimensions of Wood Screws 180 

4V. Lag Screws, Size and Weight 181 

48. Holding Power of Screws 181 

49. Drift-bolts, Holding Power:of 184 

50. Standard Dimensions of Screws, Heads, and Nuts 185 

5L Weight of Bolts and Nuts 186 

52. Weight and Strength of Bolts 187 

53. Thickness and Weight of Washers 187 

54. Length of Rivet-shank required to Form Head 189 

55. Weight of Rivets 191 

56. Natural Slopes of Earth 199 

57. Lengths and Angles of Slopes 199 

58. Amount of Cement and Sand required for One Cubic Yard of Mortar 245 

59. Weight of Flat Dense-tile Arches 304 

60. Weight of Porous Tile Arches 304 

61. Number and Weight of Shingles per Square 309 

62. Dimensions and Number of Slates per Square 312 

63. Galvanized Iron, Weight per Square Foot 313 

64. Weight of Roof -coverings 314 

65. Weight of Lead Waste-pipe 317 

156. Weight and Thickness of Lead Pipe 318 

1)7. Weight of Plain and Galvanized Iron Pipe 319 

iS8. Weight of Block-tin Pipe 320 

/)9. Weight of Cast-iron Soil-pipe 320 

70. Quantity of Materials required for Plastering 335 

71. Area covered with One Cubic Foot of Cement and Sand 335 

72. Thickness and Weight of Sheet Glass 339 

73. Thickness and Weight of Skylight Glass 339 

74. Dimensions and Weight of Cast-iron Pipes 360 

75. Weight of Standard Specials 362 

76. Weight of Lead and Gasket required for Each Joint of Cast-iron 

Pipe 363 

77. Length of Sewer-pipe One Barrel of Cement will lay 370 

78. Weight of Salt-glazed Sewer-pipe 370 

79. Inches in Decimals of a Foot 394 

80. Specific Gravity and Weight of Materials 396 

81. Areas and Circumference of Circles 411 

82. Square and Cube Roots of Numbers 416 

83. Logarithms of Numbers 433 

84. Natural Sines, Tangents, and Secants 463 

86. Tangents and Cotangents 487 



INSPECTION OF THE MATERIALS AND WORKMAN- 
SHIP EMPLOYED IN CONSTRUCTION. 



CHAPTER I. 
DUTIES OF INSPECTORS. 

The duty of the inspector is to see that the work on which he 
is placed is constructed in accordance with the plans and specifi- 
cations therefor and such written or verbal instructions as he 
may from time to time receive from his superior officer. 

To perform his duty efficiently he must make himself thoroughly 
acquainted with the requirements of the specifications, a copy of 
which should always be in his possession. 

The details of the inspector's duty will vary with the character 
of the work. In a general way it may be divided into three parts, 
as • 

1. Inspection of the materials to be employed. 

2. Inspection of the methods used in preparing the materials. 

3. Inspection of the construction, or placing of the prepared 
materials in the structure. 

To efiiciently perform each of these functions the inspector 
must be familiar with the characteristics of the materials with 
which he has to deal, the methods employed in preparing and 
placing them in the work, and he must also know whether the 
finished work is what is required or expected. 

In performing the first section of his duty the inspector is re- 
quired to pass upon the quality of the materials delivered, and 
determine whether they meet the roquiremonts of the specifications 
or not, rejecting all that are defective. 

In marking rejected material he must be ^.areful to so place the 



2 DUTIES OF INSPECTORS. 

marks that they cannot be readily erased. As a distinguishing 
mark, the letter " R " or *' C " may be used. 

It will not be sufficient only to mark the rejected material and 
rely upon its being removed by the contractor. He must see that 
it is removed. If this precaution is not taken, the chances are that 
part if not all of it will find its way into the work. 

A careful record of all material rejected should be kept, stating 
the kind, character of the defects, and amount. 

Under the second division of his duty the inspector has to watch 
the methods employed in preparing the materials, to see that the 
quantities called for are used, and that the dimensions of all manu- 
factured pieces correspond to those marked on the plans. 

The right of the inspector to require special methods of manu- 
facture to be followed is not always clearly defined. It is 
customary to allow the contractor to follow his own methods, so 
long as such methods cause no injury to the material and produce 
the required results. But when such methods cause injury or fail 
to produce the required results the inspector should have them 
stopped. 

To efficiently perform his duty under the third section the in- 
spector must be familiar with the methods employed by the vari- 
ous craftsmen in executing their work. 

To provide against slighting by careless and indifferent work- 
men constant vigilance is necessary, especially in such parts of 
the work which are difficult of access or will be covered up. 

A close scrutiny of each workman's manner of doing his work 
will be a great aid in directing attention to defective workmanship. 
Every craftsman whose workmanship is once found defective 
should be closely watched, and if found to persist in doing defec- 
tive work his removal should be ordered. 

The specifications and plans for each particular work must be 
the inspector's guide as to the character of the materials and work- 
manship required, and in case of any discrepancy between them, 
or doubt as to the meaning of any of the clauses, the matter must 
be submitted without delay to the engineer or architect for an 
explanation. 

The inspector should keep a diary recording the state of the 
weather, the number and trade of the workmen employed, the 
orders received and given, the amount and kind of material 
delivered, ace 'pted, and rejected, tlie progress made, accidents, 
and any other incident which circumstances may suggest. 

At the periods directed by his chief he will send in his report. 



DUTIES OF INSPECTORS. 3 

This report is made up from the record of daily events, and should 
give such full details, figures, and descriptions as will enable the 
chief to judge of the progress of the work. 

The inspector should so arrange his work as to inconvenience 
the contractor as little as possible. He should be on hand at all 
times so that workmen can consult him about any questionable 
points as they arise, and in this way avoid a great deal of friction 
which might occur if they proceeded in the way that seemed best 
to them. 

On the failure of the contractor or any of his workmen to 
comply with the requirements of the specifications, the inspector 
should notify him or his representative of the defective work and 
allow him a reasonable time in which to make it good. If at the 
end of this time the rectification is not made, or if he refuses to 
comply with the notice, the inspector must immediately acquaint 
his chief with the full particulars of the case, description of the 
defective work, character of the order given, and reasons advanced 
by the contractor for refusing to conform to it. 

The inspector should avoid arguments and disputes, and before 
raising objections or making complaints he should be quite sure 
of his case, then in as few words as possible make the complaint 
known. When complaint is necessary it should be promptly 
made; the longer it is put off the more difficult will be the 
rectification. 

The disagreements most frequent between inspectors and con- 
tractors and their agents are caused chiefly by complaints of the 
former of non-performance of the work in accordance with the 
specifications, and, on the part of the latter, complaints of undue 
severity. This complaint is to be expected; the best of men are 
reluctant to change what has already been done, and if inadver- 
tence or temporary convenience has led them Into an obvious 
violation of the specifications, they will mince the truth in their 
explanations and excuses. 

The adjusting of these disagreements,the inspector, unless he be 
possessed of a large fund of amiability and common sense, will 
find a very trying and unpleasant task. He who can distinguish 
between a mere blemish and a real defect, and thoroughly under- 
stands his position and can maintain it with firmness, will be less 
likely to have bad work thrust at him than one who errs in his 
decisions or is irresolute in his position. 



CLASSIFICATIOI!^ OF STOiTES. 



CHAPTER IL 
STRUCTURAL MATERIALS. 

L NATURAL STONES. 

Classification of Stones. 

The rocks from whicli the stones for building are selected are 
classified according to (1) tlieir geological position, (2) their 
physical structure, and (3) their chemical composition. 

Geological Classification. — The geological position of 
rocks has but little connection with their properties as building 
materia' s. As a general rule, the more ancient rocks are the 
stronger and more durable ; but to this there are many notable 
exceptions. According to the usual geological classification rocks 
are divided into three classes, viz. : 

Igneous, of which greenstone (trap), basalt, and lava are ex- 
amples. 

MetamorpliiCy comprising granite, slate, marble, etc. 

Sedimentary, represented by sandstones, limestones, and clay. 

Physical Classification. — With respect to the structural 
character of their large masses, rocks are divided into two great 
classes : (1) the unstratified, (2) the stratified, according as they 
do or do not consist of flat layers. 

The unstratified rocks are for the most part composed of an 
aggregation of crystalline grains firmly cemented together. Granite, 
trap, basalt, and lava are examples of this class. All the unstrati- 
fied rocks are composed as tit were of blocks which separate from 
each other when the rock decays or when struck violent blows. 
These natural joints are termed the line of cleavage or rift, and in 
all cutting or quarrying of unstratified rocks the work is much 
facilitated by taking advantage of them. 

The stratified rocks consist of a series of parallel layers, 
evidently deposited from water, and oriirinallv horizontal, al- 
though in most cases they have become nior<^ or less inclined and 
curved by the action of disturbing forces, it is easier to divide 



REQUISITES FOR GOOD BUILDIKG STONE. 5 

them at the planes of division between these layers than else 
where. They are traversed by veins or cracks, sometimes empty, 
sometimes containing crystals, sometimes filled with *' dikes," or 
masses of unstratified rock. These veins or dikes are often ac- 
companied by a "fault'' or abrupt alteration of the level of the 
strata. Besides its principal layers or strata, a mass of stratified 
rock is in general capable of division into thinner layers ; and, 
although the surfaces of division of the thinner layers are often 
parallel to those of the strata, they are also often oblique or even 
perpendicular to them. This constitutes a laminated structure. 

Laminated stones resist pressure more strongly in a direction 
perpendicular to their laminae than parallel to them; they are 
more tenacious in a direction parallel to their laminae than per- 
pendicular to them ; and they are more durable with the edges 
than with the sides of their laminae exposed to the weather. 
Therefore in building they should be placed with their laminae or 
** beds" perpendicular to the direction of greatest pressure, and 
^ith the edges of these laminae at the face of the wall. 

Chemical Classification. — The stones used in building 
are divided into three classes, each distinguished by the pre- 
dominant mineral which forms the chief constituent, viz. : 

Silicious stones, of which granite, gneiss, and trap are examples. 

Argillaceous stones, of which clay, slate, and porphyry are 
examples. 
^ Calcareous stones, represented by limestones and marbles. 

Requisites for Good Building' Stone. 

The requisites for good building stone are durability, strength^ 
cheapness, and beauty. 

Durability — The durability of stone is a subject upon which 
there is very little reliable knowledge. The durability will de- 
pend upon the chemical composition, physical structure, and the 
position in which the stone is placed in the work. The same stone 
will vary greatly in its durability according to the nature and ex- 
tent of the atmospheric influences to which it is subjected. 

The sulphur acids, carbonic acid, hydrochloric acid, and traces 
of nitric acid, in the smoky air of cities and towns, and the carbonic 
acid in the atmosphere of the country ultimately decompose any 
stone of which either carbonate of lime or carbonate of magnesia 
forms a considerable part. 

Wind has a considerable effect upon the durability of stone. 



6 TESTS FOR STOKE. 

Higli winds blow sLarp particles against tlie face of the stone and 
thus grind it away. Moreover, it forces the rain into the pores 
of the stone, and may thus cause a considerable depth to be sub- 
ject to the effects of acids and frost. 

In winter water penetrates porous stones, freezes, expands, and 
disintegrates the surface, leaving a fresh surface to be similarly 
acted upon. 

Strength is generally an indispensable attribute, especially 
under compression and cross-strain. 

Cheapness is influenced by the ease with which the stone can 
be quarried and worked into the various forms required. Cheap- 
ness is also affected by abundance, facility of transportation, and 
proximity to the place of use. 

Appearance. — The requirement of beauty is that it should 
have a pleasing appearance. For this purpose all varieties contain- 
ing much iron should be rejected as they are liable to disfigure- 
ment from rust-stains caused by the oxidation of the iron under 
the influence of the atmosphere. 

Tests for Stone. 

The relative enduring qualities of different stones are usually 
ascertained by noting the weight of water they absorb in a given 
time. The best stones as a rule absorb the smallest amount of 
water. 

To determine the absorptive power, dry a specimen and weigh 
it carefully, then immerse it in water for 24 hours and weigh 
again. The increase in weight will be the amount of absorption. 

Table 1. 

ABSORPTIVE POWER OF STONES. 

Percentage of 
Water absorbed. 

Granites 0.06 to 0.15 

Sandstones..., 0.41 " 5.48 

Limestones 0.20 " 5.00 

Marbles 0.08 *' 0.16 

Effect of Frost {BrarcTs I'est). — To ascertain the effect of 
frost, small pieces of tlie stone are immersed in a concentrated 
boiling sohilion of sul[)batL^ of soda ((Haubor's salts), and iben 
hung u}) for a tew days in tlie air. 

The salt crystallizes in the jion^s of the stone, sometimes foicing 



PRESERVATION OF STONE. 7 

off bits from the corners and arrises, and occasionally detaching- 
larger fragments. 

The stone is weighed before and after submittiDg it to the test. 
The difference of weight gives the amount detached by disintegra- 
tion. The greater this is, the worse is the quality of the stone. 

Effect of the Atmosphere (Acid Test). — Soaliing a stone 
for several days in water containing 1 per cent of sulphuric and 
hydrochloric acids will afford an idea as to whether it will stand 
the atmosphere of a large city. If the stone contains any matter 
likely to be dissolved by the gases of the atmosphere, the water 
will be more or less cloudy or muddy. 

A drop or two of acid on the surface of a stone will crer.te an in- 
tense effervescence if there is a large proportion present of carbon- 
ate of lime or magnesia. 

Preservation of Stone. 

There are a great many preparations that have been used for 
the prevention of the decay of building stones, as paint, coal-tar, 
oil, beeswax, rosin, paraffine, soft-soap, soda, etc. All of the 
methods are expensive, and there is no evidence to show that they 
afford permanent protection to the stone. 

Ransome's Process consists in. coating the surface of the 
stone first with a solution of silicate of soda or potash, and then 
with a solution of chloride of calcium or barium. The chemical 
reaction produces insoluble silicate of lime and chloride of sodium, 
which washes out. 

The surface of the stone to be coated is made thoroughly clean 
and dry, all decayed parts being cut oat and replaced by good. 

The silicate is diluted with from 1 to 3 parts of soft water until 
it is thin enough to be absorbed by the stone freely. The less 
water that is used the better, so long as the stone is thoroughly 
penetrated by the solution. 

The solution is applied with an ordinary whitewash brush. 
After about a dozen brushings over, the silicate will be found to 
enter very slowly. V^hen it ceases to go in, but remains on the 
surface glistening, although dry to the touch, it is a sign that the 
stone is sufficiently charged ; the brushing on should stop just short 
of this appearance. No excess must on any account be allowed to 
rcnain on the face. After the silicate hns hocome perfectl?/ dry 
the solution of chloride of calcium is a])pli(Ml freely (but bruslied on 
lightly, without making it frotfi) so as lo be absorbed with the sili- 
cate into the structure of the stone. 



8 SlLICIOUS STONES. 

Special care must be taken not to allow either of tlie solutions 
to be splashed upon windows or painted work, as the stains can- 
not be removed. 

The brushes or jets used for the silicate must not be used for 
the chloride, or vice versa. 

About four gallons of each solution is required for every hun- 
dred square yards of surface, but this will depend upon the 
porosity of the stone treated. 



11. DESCRIPTION OF BTTILDINa STONES. 

Silicious Stones, 

Granite is an unstratified rock composed of silica or quartz, 
feldspar, and mica. In addition to these essential constituents 
one or more accessory minerals may be present ; the more com- 
monly occurring are hornblende, pyroxene, epidote, garnet, tour- 
maline, magnetite, pyrite, and graphite. The character of the 
rock is often determined by the presence of these accessory con- 
stituents in quantity. 

Granite varies in texture from very fine and homogeneous to 
coarse porpliyritic rocks in which the individual grains are an 
inch or more in length. The color is also dependent upon the 
minerals present ; if the feldspar is the orthoclase (potash spar), 
it communicates a red color; the soda-spar produces gray. The 
mica also plays an important part in the modification of color ; if 
it is the white muscovite, it produces no change, but if the black 
biotite mica be present, it modifies the color accordingly. Horn- 
blende gives a dark mottled appearance ; pyroxene also gives a 
dark appearance ; epidote communicates a green color. 

The durability of the granites is closely related to their miner- 
alogical composition. The presence or absence of certain species 
influences the hardness and homogeneous nature of the stone. 
Although popularly regarded as the most durable stone, there are 
some notable exceptions. The quartzose varieties are brittle, the 
feldspathic are easily decomposed; feldspar in excess causes 
rapid decay and disintegration in consequence of the action of air 
and water on the potash which seems to be removed, and the 
residue falls into a white powder con.posed chiefly of silica and 
alumina. The micaceous varieties a)<' easily laminated. 

The durability and hardness of granites are greater the more 



SILICIOUS STONES. 9 

quartz and hornblende predominate, and the less the quantity of 
feldspar and mica, which are the more weak and perishable in- 
gredients. Smallness and lustre in the crystals of feldspar in- 
dicate durability, largeness and dulness the reverse. 

If the mica or feldspar contains an excess of lime, iron, or 
soda, the granite is liable to decay. 

The quantity of iron either as the oxide or in combination with 
sulphur will affect the durability. 

The iron can generally be seen with a good glass; and a very 
short exposure to air, especially if assisted in dry weather by 
sprinkling with water to which has been added 1 per cent of 
nitric acid, will reveal it. 

The name *' granite " as popularly used is not restricted to rock 
species of this name in geological nomenclature, but includes 
what are known as gneisses (foliated and bedded granites), syenite, 
gabbro, and other crystalline rocks whose uses are the same; in 
fact, the similar adaptability and use have brought these latter 
species into the class of granites. The name is also often im- 
properly applied to the diabase and trap rocks. 

The term ** syenite" is usually restricted by modern petrog- 
raphers to a rock which is an aggregate of orthoclase and horn- 
blende; in other words, a granite in which the quartz has dis- 
appeared, while the mica has been superseded by hornblende. 

Gneiss and Mica-slate consist of the same materials as 
granite, but in a stratified form. They are found in the neighbor- 
hood of granite, in strata much inclined, bent, and distorted, and 
often form great mountain masses. Gneiss resembles granite in 
its appearance and properties, but is less strong and durable. 
Mica-slate is distinguished by containing little or no feldspar 
so that it consists chiefly of quartz and mica. 

Trap (Greenstone) and Basalt. — These are unstratified 
metamorphic rocks, and consist of granular crystals of hornblende 
or augite with feldspar. In trap the grains are considerably 
finer than in granite; in basalt they are scarcely distinguishable. 
Trap breaks up into small blocks, basalt into regular prismatic 
columns. Both these rocks are very compact, hard, tough, and 
durable; being generally without cleavage or bedding they are 
exceedingly intractable under the hammer or chisel, and conse- 
quently their use in masonry is very limited. 

The ** Palisades " on the western shore of the Hudson River, 
opposite and above New York, are composed of trap rock, which 



1^ SILICIOUS STOITES. 

splits easily into small blocks raucli used for paving under 
the name of -Belgian block/' Crushed trap rock is also exten- 
sively used for makmg macadam pavements. 

Sandstones are stratified rocks consisting of grains of sand, 
that is, small crystals of quartz cemented together by silicious,* 
ferruginous, calcareous, or argillaceous material. From the 
nature of the cementing material the rocks are variously 
designated as ferruginous, calcareous, etc. 

The hardness, strength, and durability depend upon the nature 
of the cementing material; if it be one which decomposes readily, 
as in the argillaceous and calcareous varieties, the whole mass is 
soon reduced to sand. When composed of nearly pure silica and 
well cemented, sandstones are as resistant to weather as granite, 
and very much less affected by the action of fire. When quarried 
they are usually saturated with quarry- water (a weak solution of 
silica) and are very soft, but on exposure to the air (called 
"seasoning") they become harder by the precipitation of the 
soluble silica. 

The Color of sandstone is determined by the cementing material. 
A stone composed exclusively of grains of quartz, without foreign 
matter, is snow-white. The various shades of red and yellow are 
produced by the iron oxides; the purple tints are due to oxide of 
manganese; the gray, blue, and green tints are produced by iron 
in the form of ferrous oxide, carbonate, or silicate ; the brown 
color is produced by the hydrated oxide of iron. 

Sandstones are in general porous and capable of absorbing much 
water, but they are comparatively little injured by moisture, 
except when built with the layers set on edge, in which case the 
expansion of water in freezing between the layers makes them 
split or ''scale" off from the face of the stone; when built on the 
natural bed any water which may penetrate between the edges of 
the layers has room readily to expand or escape. 

When there is much lime in the cementing matter of the sand- 
stone it decays rapidly in the atmosphere of the seacoast, and in 
that of towns where much coal is burned; in the former case the 
lime is dissolved by muriatic acid, in the latter by sulphuric acid. 
Crystals of sulphuret of iron are sometimes embedded in the stone, 
which, when exposed to air and moisture, decompose and cause 
disintegration. These crystals are easily recognized by their 
yellow or yellowish-gray color and metallic lustre. 

On account of its easy working qualities it has been named 



AEGILLACEOUS STONES. 11 

" freestone " by stone-cutters. A great variety of other names are 
applied, derived from the appearance of the stone and the uses to 
which it is put. 

Arg-illaceous Stones. 

Slate. — Clay-slate is a primary stratified rock of great hard- 
ness and density, with a laminated structure making in general a 
great angle with the planes of its stratification. It splits readily 
along planes called ''planes of slaty cleavage." This facility of 
cleavage is one of the most valuable characteristics, as it enables 
masses to be split into slabs and plates of small thickness and 
great area. 

The color of slates varies greatly; those most frequently met 
with are dark blue, bluish black, purple, gray, bluish gray, and 
green. Red and cream-colored slates are also occasionally found. 

Some slates are marked with bands or patches of a different 
color; e.g., dark purple slates often have large spots of light green 
upon them. These are generally considered not to injure the 
durability of the slate, but they lower its quality by spoiling its 
appearance. 

Ribs or wins are dark marks running through some slates. 
They are always objectionable, but particularly when they run in 
the direction of the length of the slate, for it will be very liable 
to split along the vein. These veins and ribbons are frequently 
soft and of inferior quality to the slate proper. On exposure to the 
weather they effloresce and show signs of decomposition due to 
the sulphate of iron contained in them. Such slates should not 
be allowed in good work. 

Calcareous Stones. 

Limestones are composed of carbonate of lime combined 
with various minerals. There are many varieties, which differ 
in color, composition, and value for engineering and building 
purposes. The several kinds are usually designated by the name 
of the principal combined minerals. Thus, if it contains much 
sand it is called silicious limestone; if the silica is very fine 
grained it is called hornstone ; if the silica is distributed in 
nodules or flakes, either in seams or throughout the mass, it 
is cherty limestone ; if it contains silica and clay in about 



12 CALCAREOUS STOi^ES. 

equal proportions it is liydraulic limestone ; if claj alone is the 
principal ingredient it is argillaceous limestone ; if iron is the 
principal impurity it is ferruginous limestone ; if iron and clay 
exceed the lime it is ironstone; if the ironstone is decomposed and 
the iron hydrated it is roitenstonc ; if carbonate of magnesia forms 
one third or less it is magnesian limestone; if carbonate of mag- 
nesia forms more than one third it is dolomitic limestone. 

Granular Limestone consists of carbonate of lime in grains, 
which are in general shells, or fragments o?^shells, cemented 
together by some compound of lime, silica, and alumina, and 
often mixed with a greater or less quantity of sand. It is always 
more or less porous. It is found in various colors, especially 
white and light yellowish brown. In many cases it is so soft 
when first quarried that it can be cut with a knife, and hardens 
by exposure to the air. It is found in various strata, especially 
the oolitic formation. 

Compact Limestone consists of carbonate of lime, either pure, 
or mixed with sand and clay. It is generally devoid of crystalline 
structure, of a dull earthy appearance, and of a dark blue, gray, 
black, or mottled color. In some cases, however, it is crystalline 
and full of organic remains. It is then known as crystalline 
limestone. 

Magnesian and Dolomitic Limestones. — When the carbon- 
ate of magnesia is present in limestone to the amount of one third 
or less it is called magnesian limestone; when the carbonate of 
magnesia forms one third or more it is called dolomitic lime- 
stone. Both kinds are found in various conditions, from the com- 
pact crystalline to the porous granular condition. The durability 
depends mainly on the texture; when that is compact they are 
extremely durable. When sand is present in the magnesian 
variety the weathering qualities are greatly injured. Some 
varieties are peculiarly subject to the attacks of sulphuric acid, 
which forms a soluble sulphate of magnesia easily washed away. 

Marble is the purest form of carbonate of lime (except stalac- 
tites), and is an earlier formation of limestone, with a pressure 
which retained the carbonic acid. The name marble is generally 
applied to any limestone which will take a good polish. Marbles 
exhibit great diversity of color and texture; they are chiefly used 
for ornamentation and interior decorations. 



NATURAL STONE. 



13 



Table 2. 
SPECIFIC GRAVITY, WEIGHT, AND RESISTANCE TO CRUSHING OF 

VARIOUS STONES. 
Granites. 



Localities. 



Min. 
Max 



Kirtland Rocks, Conn 

Lord's Island, " 

Mystic River, ** ......... 

New Haven, " 

Millstone Point, ** 

Milford, " 

New London, ** 

Sharkey's Quarry, Me 

Hurricane Island, ** 

Fox Island (blue), ** =..., 

Vinal Haven (gray), ** 

Huron Island, Mich 

Duluth (dark), Minn 

'' (light), - 

East St. Cloud. " 

Quincy (dark). Mass 

'' (light), '* 

Fall River (gray), " 

Cape Ann, ** 

Port Deposit, Md 

Patapsco, * * 

Jersey City, N. J 

Passaic Co. (gray), N. J , . 

Chaumont Bay, N Y 

Westchester Co., ** 

Garrison's (gray), '* 

Staten Island (blue), * * 

Keene (bluish gray), N. H 

Gunnison, Colo 

Platte Canon (red), Colo 

Richmond, Va < 

Westerly (gray), R. I 

Burnet Co., Tex > . . . . 

Aberdeen, Scotland (gray) 

(red) 

Gneiss, Conn . 

Syenite, Fourth Mountain, Ark. 

Trap, Jersey City, N. J 

" Palisades, *' 

•* Staten Island, N. Y , 





Average 


Specific 
Gravity. 


Weight. 
Pounds per 
Cubic Foot. 


2.60 


163 


2.80 


176 


2.66 


166 


2.63 


164 


2.70 


169 


2.66 


166 


2.72 


170 


2.67 


167 


2.66 


166 


2.64 


163 


3.03 


189 


2.65 


162 


2.65 


166 


2.58 


161 


2.86 


179 


2.65 


166 




164 


(2.72 
(2.63 


170 


164 


2.67 


167 


2.82 


176 


2.62 


163 


2.62 


165 


2.70 


168 


2.64 


167 


3.03 


jl78 
(189 


2.86 


178 



Resistance to 

Crushing. 

Pounds per 

Square Inch. 

12,000 

35,000 

35,000 
24,000 
22,250 
9,750 
16,187 
22,600 
12,500 
22,125 
15,000 
14,875 
IS.OOOto 18,000 

20,650 
17,750 
19,000 
28,000 
19,500 
14,750 
15,937 
12,423 
19,500 
19,750 
5,340 
20,750 
24,040 
22.700 
18,250 
13,370 
22,250 
12,875 
13,000 
14,600 
14,100 
21,250 
14,937 
11,891 
10,900 
10,760 
19,600 
30,740 
20,000 
24,000 
19,700 
22,250 



14 



NATURAL STOi^E. 



SPECIFIC GRAVITY, WEIGHT, AND RESISTANCE TO CRUSHING OF 

VARIOUS STONES. {Continued.) 

Sandstones. 



Localities. 

Min. 
* Max. 


Specific 
Gravity. 

2.23 

2.75 


Average 

Weight. 

Pounds per 

Cubic Foot. 

137 
170 


Resistance to 

Crushing. 

Pounds per 

Square Inch. 

5,000 
18,000 


Potsdam (red), N. Y. 


2.60 
2.75 
2.41 
2.68 
2.42 
2.25 
2.71 
2.13 
2.26 

2.57 
2.16 

2.24 

2.14 

2.89 

j 2.36 

■(2.62 

2.63 
2.32 

2.22 
2.58 
2.61 


162 
171 
151 
167 
151 
141 
169 
183 
147 
148 

160 

135 

140 

134 
149 
147 
163 

164 
145 

188 
158 
157 

140 
173 


42,804 


Maiden (bluestoneV '* 




Medina (pink) '* 


17,725 


Warsaw (bluestone), ** 


Albion (brown), ** 


13,500 
9,850 

13,472 
4,850 

11,700 

18,310 
3 7,250 
( 10,250 
8,850 
8,750 
6,800 
6,650 
5,000 
9.687 
6,950 

13,000 

9,150 
10,700 
6,250 
8,750 
6,250 
7,450 


Little Falls (brown), " 


Oxford (bluestone), ** 


Haverstraw (red) * * 


Belleville (gray), N. J 


*' (brown), '* , 

Berea (drab), Ohio. . . . 

Vermillion (drab), *' . . . . 
Massillon (yellow drab), *' ... 

Cleveland (olive-green), ** 

North Amherst, " .... 
Seneca (red brown), *' .... 
Warrensburg (bluish drab). Mo.. 

Middletown (Portland), Conn 

Dorchester (brown). New Bruns- 
wick 


Kasota (pink), Minn 

Frontenac (light buff), " 

Fond du Lac, ** 

Fond du Lac (purple). Wis 

Marquette, Mich 


Bristo w, Va 


5,714 


Long Meadow (reddish brown), 
Mass , 


( 7,000 

} 14.000 

12,810 


Humnielstown, Pa 


Manitou (light red), Colo 

St. Vrain, " 

Fort Collins (gray), *' 

SLATE. 

Northampton Co., Pa 


( 6,000 

\ 11,000 

11,505 

11,707 







NATURAL STONE. 



15 



SPECIFIC GRAVITY, WEIGHT, AND RESISTANCE TO CRUSHING OF 

VARIOUS STONES. (Continued.) 

Limestones. 



Localities. 



Min. 
Max. 



Glens Falls, N. Y 

North River, *' 

Lake Champlain, *' 

Canajoharie, ** 

Erie Co. (blue), '* 

Kingston, ** 

Garrison's, ** 

Joliet (white), 111 

Grafton (magnesian). 111 , 

Marblehead (white), Ohio 

Marquette (drab), Mich , 

Lime Island (drab), *' 

Billings ville. Mo , . . , 

Cooper Co, (dark drab), Mo . . . . 
Bardstown (dark), Ky 

Sturgeon Bay (bluish drab). Wis, 

Bedford, Ind 

Salem, ** 

Red Wing, Minn 

Stillwater, ** , 

Avondale (gray), Pa 

(liglit), '' 

Conshohocken * * 





Average 


Specific 
Gravity. 


Weight. 
Pounds per 
Cubic Foot. 


1.90 


118 


2.75 


175 


2.70 


169 


2.71 


169 


2.75 


172 


2.68 


168 


2.64 


165 


2.69 


168 


2.63 


165 


2.54 


159 


2.40 


150 


2.34 


146 


2.50 


156 


2.32 


141 


2.69 


168 


2.78 


174 



Resistance to 

Crushing. 

Pounds per 

Square Inch. 

7,000 

20,000 



11,475 

13,425 

25,000 

20,700 

12,250 

13,900 

18,500 

16,900 

17,000 

12,600 

8,050 

; 18,000 

' 25,000 

7,250 

6,650 

16,250 

21,500 

{ 6,000 

1 10,000 

8,625 

23,000 

10,750 

18,000 

12,112 

14,090 

16,340 



Marbles. 



Min 
Max. 



East Chester, N. Y. 
Hastings, ** . 

Dorset, Vt 

Rutland, ** 

Mill Creek, 111 



Montgomery (blue), Pa. 

North Bay, Wis 

Montgomery, Va 

Lee, Mass 



Stockbridge, Mass. 

Colton, Cal 

Italy 



2.62 
2.95 

2.87 


165 
179 

179 


2.63 


165 


2.57 


172 


2.80 


175 


2.69 


168 



8,000 
20,000 

13,504 

18,941 

7,612 

10,746 

9,687 

j 9,590 

( 13,700 

20,025 

8,950 

(20,504 

(22,700 

10.382 

17,783 

13,425 



16 NATURAL STONE. 



Inspection of Stone. 

The fitness of stone for structural purposes may be determined 
approximately by examining a fresh fracture, the appearance and 
characteristics of which are as follows : 

The even fracture occurs when the surfaces of division are 
planes in definite positions, and indicates a crystalline structure. 

The uneven fracture presents sharp projections, and is character- 
istic of a granular structure. 

The slaty fracture occurs when the planes of division are par- 
allel to the lamination and are uneven for other directions of 
division. 

The conchoidal fracture presents smooth concave and convex 
surfaces, and is characteristic of a hard and compact structure. 

The earthy fracture leaves a rough dull surface, and indicates 
softness and brittleness. 

Stones which contain '*drys," i.e., seams containing material 
not thoroughly cemented together, or ** crowfoots" i.e., veins 
containing dark-colored uncemented material, should be rejected. 

To test the soundness of any stone, strike it smart blows with a 
light hammer on both beds ; if it rings clearly, it is sound ; if the 
sound is dull, it is seamy and should be rejected. 

Stones to be used for face work should be closely examined for 
seams, the effect of which is to allow rain-water to penetrate to 
the interior of the stone and, under the action of frost, to split and 
crack it. 

The Defects op Granite are termed knots ^ sap, sTiakes, and 
rot. Knots are lumps of different color from the main body ; they 
are usually black or white. Sap is the name given to discolorations 
or stains. Shakes are seams which usually have discolored edges. 
Mot is the name given to stone which crumbles easily. 

Sandstones and Limestones must be closely examined for 
seams, holes, and cavities filled with sand, clay, or uncemented 
material. 

The appearance of good sandstone is characterized by the sharp- 
ness of the grains, smallness of the cementing material, and a clear 
shining, translucent appearance on a newly broken surface. 
Rounded grains and a dull mealy surface indicate soft and perish- 
able stoue. 



II 



NATURAL STONE. 17 

Quarrying. 

In quarrying stone for building purposes there sliould be as 
little blasting as possible, as it shakes the stone. Stone showing 
powder-cracks should be rejected. 

Weather-worn stone and stone from the outcrop or capping of 
a quarry should not be used in good work. Stone should if pos- 
sible be worked at once after being quarried, for it is then easier 
to cut. 

The quarrying of limestone, marble, and sandstone during winter 
is not advisable, as they are liable to be injured by the freezing of 
the contained water. 

Seasoning. 

Stones of a porous nature which contain water when quarried 
are said to be green or sappy. Such stones must be exposed to 
the drying action of the air before using them, otherwise they 
will be split and fractured by the action of frost upon the con- 
tained water. 



18 ARTIFICIAL STORES. 

Ill, ARTIFICIAL Stones. 
Brick. 

Brick is an artificial stone made by submitting clay, which has 
been suitably prepared and moulded into shape, to a temperature 
of sufficient intensity to convert it into a semi-vitrified state. 

The quality of the brick depends upon the kind of clay used 
and upon the care bestowed on its preparation. 

The clays of which brick is made are chemical compounds con- 
sisting of silicates of alumina, either alone or combined with 
other substances, such as iron, lime, soda, potash, magnesia, etc., 
all of which influence the character and quality of the brick, ac- 
cording as one or the other of those substances predominates. 

Iron gives hardness and strength ; hence the red brick of the 
Eastern States is often of better quality than the white and 
yellow brick made in the West. Silicate of lime renders the clay 
too fusible and causes the bricks to soften and to become distorted 
in the process of burning. Carbonate of lime is at high tempera- 
tures changed into caustic lime, renders the clay fusible, and 
when exposed to the action of the weather absorbs moisture, 
promotes disintegration, and prevents the adherence of the mor- 
tar. Magnesia exerts but little influence on the quality ; in small 
quantities it renders the clay fusible ; at 60° Fahr. its crystals lose 
their water of crystallization, and cold water decomposes them, 
forming an insoluble hydrate in the form of a white powder. In 
air-dried brick this action causes cracking. The alkalies are 
found in small quantities in the best of clays; their presence tends 
to promote softening, and this goes on the more rapidly if it has 
been burned at too low a temperature. Sand mixed with the clay 
in moderate quantity (one part of sand to four of clay is about the 
best proportion) is beneficial, as tending to prevent excessive 
shrinking in the fire. Excess of sand destroys the cohesion and 
renders the brick brittle and weak. 

Manufacture of Brick. 

The manufacture of brick may be classified under the following 
heads : 

Excavation of the clay, either by manual or mechanical power. 

Preparation of the clay consists in {a) removing stones and me- 
chanical impurities ; {!)) tempering and moulding, which is now 



BRICK. 19 

done almost wholly by machinery. There is a great variety of 
machines for tempering and moulding the clay, which, however, 
may be grouped into three classes, according to the condition of 
the clay when moulded : (1) soft-mud machines, for which the 
clay is reduced to a soft mud by adding about one quarter of its 
volume of water ; (2) stiff-mud machines, for which the clay is 
reduced to a stiff mud ; (3) dry-clay machines, with which the dry 
or nearly dry clay is forced into the moulds by a heavy pressure 
without having been reduced to a plastic mass. These machines 
may also be divided into two classes, according to the method of 
filling the moulds : (1) those in which a continuous stream of 
clay is forced from the pug-mill through a die and is afterwards 
cut up into bricks ; and (3) those in which the clay is forced into 
moulds moving under the nozzle of the pug-mill. 

Drying and Burning.— The bricks, having been dried in the 
open air or in a drying-house, are burned in kilns ; the time of 
burning varies with the character of the clay, the form and size 
of the kiln, and the kind of fuel, from six to fifteen days. 

Color of Bricks. 

The color of bricks depends upon the composition of the 
clay, the moulding sand, temperature of burning, and volume of 
air admitted to the kiln. Pure clay free of iron will burn white ^ 
and mixing of chalk with the clay will produce a like effect. 
Iron produces a tint ranging from red and orange to light yellow, 
according to the proportion of the iron. 

A large proportion of oxide of iron mixed with pure clay will 
produce a bright red, and where there is from 8 to 10 per cent, 
and the brick is exposed to an intense heat, the oxide fuses and 
produces a dark blue or purple, and with a small volume of man- 
ganese and an increased proportion of the oxide the color is 
darkened even to a black. 

A small volume of lime and iron produces a cream color, an in- 
crease of iron produces red, and an increase of lime bi'own. 

Magnesia in presence of iron produces yellow. 

Clay containing alkalies and burned at a high temperature pro- 
duces a bluish green. 

Classification of Brick. 

Bricks are classified according to (1) the way in which they are 
moulded ; (2) their position in the kiln while being burned ; and 
(^3) their form or use. 



20 AUtlFiClAL STOKES. 

I. The method of moulding gives rise to the following terms : 
Soft-mud Brick. — One moulded from clay which has been 

reduced to a soft mud by adding water. It may be either hand- 
moulded or machine-moulded. 

Stiff-mud Brick. — One moulded from clay in the condition of 
stiff mud. It is always machine- moulded. 

Pressed Brick. — One moulded from dry or semi-dry clay. 

Re-pressed Brick. — A soft-mud brick which, after being par- 
tially dried, has been subjected to an enormous pressure. It is also 
called, but less appropriately, pressed brick. The object of the 
re-pressing is to render the form more regular and to increase the 
strength and density. 

Slop Brick. — In moulding brick by hand, the moulds are some- 
times dipped into water just before being filled with clay, to pre- 
vent the mud from sticking to them. Brick moulded by this 
process is known as slop brick. It is deficient in color and has a 
comparatively smooth surface, with rounded edges and corners. 
This kind of brick is now seldom made. 

Sanded Brick. — Ordinarily, in making soft-mud brick, sand 
is sprinkled into the moulds to prevent the clay from sticking ; the 
brick is then called sanded brick. The sand on the surface is of 
no advantage or disadvantage. In hand-moulding, when sand is 
used for this purpose, it is certain to become mixed with the clay 
and occur in streaks in the finished brick, which is very undesir- 
able. 

Machine-made Brick. — Brick is frequently described as 
'* machine-made " ; but this is very indefinite, since all grades 
and kinds are made by machinery. 

II. When brick was generally burned in the old-style up- 
draught kiln, the classification according to position was important; 
but with the new styles of kilns and improved methods of burning, 
the quality is so nearly uniform throughout the kiln that the 
classification is less important. Three grades of brick are taken 
from the old-style kiln : 

Arch or Clinker Bricks. — Those which form the tops and 
sides of the arches in which the fire is built. Being overburned 
and partially vitrified, they are hard, brittle, and weak. 

Body, Cherry, or Hard Bricks. — Those taken from the in- 
terior of the pile. The best bricks in the kiln. 

Salmon, Pale, or Soft Bricks. — Those which form the ex- 
terior of the mass. Being underburned, they are too soft for 
ordinary work, unless it be for filling. The terms salmon and pale 



BRICK. 21 

refer to the color of the hrick, and hence are not applicable to a 
brick made of a clay that does not burn red. Although nearly all 
brick-clays burn red, yet the localities where the contrary is true 
are sufficiently numerous to make it desirable to use a different term 
in designating the quality. There is not necessarily any relation 
between color, and strength and density. Brick-makers naturally 
have a prejudice against the term soft hrick, which doubtless ex- 
plains the nearly universal prevalence of the less appropriate 
term salmon. 

III. The form or use of bricks gives rise to the following classi- 
fication : 

Compass Brick. — Those having one edge shorter than the 
other. Used in lining shafts, etc. 

Feather-edge Brick. — Those of which one edge is thinner 
than the other. Used in arches ; and more properly, but less 
frequently, called wussoir brick. 

Front or Face Brick. ^ — Those which, owing to uniformity 
of size and color, are suitable for the face of the walls of buildings. 
Sometimes face bricks are simply the best ordinary brick ; but gen- 
erally the term is applied only to re-pressed or pressed brick made 
especially for this purpose. They are a little larger than ordinary 
bricks. 

Sewer Brick. — Ordinary hard brick, smooth, and regular in 
form. 

Kiln-run Brick. — All the brick that are set in the kiln when 
burned. 

Hard Kiln-run Brick.— Brick burned hard enough for the 
face of outside walls, but taken from the kiln unselected. 

Rank of Bricks. 

In regula/rity of form re-pressed brick ranks first, dry-clay brick 
next, then stiff -mud brick, and soft-mud brick last. Regularity of 
form depends largely upon the method of burning. 

The compactness and uniformity of texture, which greatly in- 
fluence the durability of brick, depend mainly upon the method 
of moulding. As»a general rule, hand- moulded bricks are best in 
this respect, since the clay in them is more uniformly tempered 
before being moulded; but this advantage is partially neutralized 
by the presence of sand-seams. Machine-moulded soft-mud bricks 
rank next in •compactness and uniformity of texture. Then come 
machine-moulded stiff-mud bricks, which vary greatly in dura- 
bility with the kind of machine used in their manufacture. By 



22 ARTIFICIAL STONES. 

some of the machines the brick is moulded in layers (parallel to 
any face, according to the kind of machine) which are not 
thoroughly cemented, and which separate under the action of 
frost. The dry-clay brick comes last. However, the relative value 
of the products made by different processes varies with the nature 
of the clay used. 

Glazed and Enamelled Bricks. 

Glazed Bricks, — Bricks are glazed by means of a composition 
of porcelain or glass which fuses and renders the surface vitreous. 
This may be done by applying a flux or a chemical solution to the 
surface. Pigments of metallic oxides are added to the composition, 
which give it any desired color or shade. The coloring is done 
either under the glaze or in the glaze. When the application is to 
be made under the glaze it is customary to dip the bricks previ- 
ously burned into a " slip" of colored clay composed, in most in- 
stances, of one part colored glass, ground, and two parts clay, the 
latter causing adhesion of the slip; the brick is then fired, or, 
after being allowed to dry, is coated with a transparent glaze and 
then fired. When the color is to be applied in the glaze the brick 
is dipped into a transparent colored glaze made of silicious sand, 
salt, and oxide of lead combined with the required coloring pig- 
ment. The composition is prepared by pulverization to a homo- 
geneous mass, then calcined, pulverized again, and made appli- 
cable by dissolving in water to the consistency of cream. The 
faces of the brick to be glazed are dipped in this solution or are 
coated with it by brushes, after which the brick is subjected to a 
temperature sufficient to fuse the glaze on the surface. 

Enamelled Bricks are generally made of a particular quality 
of clay, containing a considerable proportion of fire-clay. The 
enamel may either be applied to the unburnt brick or to the brick 
after it is burnt. In burning the enamel fuses and unites with 
the body of the brick, but does not become transparent, and there- 
fore shows its own color. It is claimed that an enamelled brick is 
more durable than a glazed brick, and will not so readily chip or 
peel. The enamel is also the purest white. 

An enamelled surface may be distinguished from a glazed sur- 
face by chipping off a piece of the brick. The glazed brick will 
show the layer of slip between the glaze and the brick ; the 
enamelled brick will show no line of demarcation between the 
body of the brick and the enamel. 



BRICK. 



23 



Table 3. 

SIZE AND WEIGHT OF BRICKS. 

The variations in the dimensions of brick render a table of 
exact dimensions impracticable. 

As an exponent, however, of the ranges of their dimensions, 
the following averages are given : 

Baltimore front j 

Wilmington *' > S^" X H" X 2f 

Washington * * ) 

Croton ** 8J"X4'' X 2J" 

Maine ordinary 7f' X 3f" X 2f" 

Milwaukee *' 8^" X ^" X ^" 

North River, N. Y 8'' X 3^ X 2^' 

English r X^" X H" 

The Standard Size as adopted by the National Brickmakers' 
A^ssociation and the National Traders and Builders' Association is 
for common brick 8J X 4 X 2i inches, and for face brick 
8| X 4|^ X 2J inches. 

Re-pressed Brick weighs about 150 lbs. per cubic foot, common 
brick 125, inferior soft 100. Common bricks will average about 
4i lbs. each. 

Hollow Brick, used for interior walls and furring, are usually 
of the following dimensions : 

Single, 8 in. long, 3f in. wide, 2i in. thick. 
Double, 8 ** *♦ 7i *' " 4i " ** 
Treble, 8 ** ** 7^ " *' 7J " " 

Boman Brick, 12 in. long, 4 to 4^ in. wide, 1 J in. thick. 



Table 4. 

SPECIFIC GRAVITY, WEIGHT, AND RESISTANCE TO CRUSHING 
OF BRICK. 



Designation of Brick. 



Best pressed. 
Common hard 
Soft 



Specific 
Gravity. 



2.4 

1.6 to 2.0 

1.4 



Weig^ht per 

Cubic Foot. 

Pounds. 



150 
125 
100 



Resistance 

to Crushing. 

Pounds per 

Square Inch. 



5,000 to 14,973 

5,000 to 8,000 

450 to 600 



24 ARTIFICIAL STOKES. — BRICK. 

Inspection of Brick. 

The characteristics of good brick are : 

1. Soundness ; that is, freedom from cracks and flaws. 

2. Hardness, to enable it to withstand pressure and strain. 

3. Begularity of shape and size ; it should have plane faces, 
parallel sides, and sharp right angled edges. 

4. Should show when broken a compact uniform structure, 
hard and somewhat glassy, and free from air-bubbles, cracks,! 
cavities, and lumps. 

5. Should emit a clear ringing sound when struck a sharpl 
blow. 

6. Should not absorb more than about -^^ of its weight of water, j 

7. The specific gravity should be 2 or more. 

8. The crushing strength of a half brick, when ground flat and^ 
pressed between thick metal plates, should be at least 7000 lbs. 
per square inch. 

9. The modulus of rupture should be at least 1000 lbs. per square 
inch. 

Good bricks are generally of a dark reddish-brown color, and 
sometimes show vitrified spots on the surface; it is not well, how- 
ever, to depend upon this fact, for it is only an indication of the 
amount of heat to which the brick has been subjected, while the 
clay of which the brick is made may be impure and ill prepared. 

Bad bricks are generally recognized by their reddish-yellow 
color, but still more by the dull sound which they emit when 
struck. Their grain being soft they crumble easily and absorb 
water with avidity. 

All brick intended for building that does not take up a small 
percentage of water is too much burned, and the mortar will 
adhere to it imperfectly. 

When a brick left in water either scales or swells, it is of bad 
quality and contains caustic lime. 

A brick which being made red hot and then having water 
poured over it does not crack is of excellent quality. 

The strength of building brick, both transverse and crushing, 
varies in tolerably close inverse ratio with the quantity of water 
absorbed in 24 hours. The strong* st bricks absorb least water. 

Good building brick absorb f ? oni to 12 per cent of water in 24 
Ijours, and with no greater absorption than 12 per cent will ordi- 
narily show from 7000 to 10,000 or more pounds per square inch 
of ultimate crushing strength, and a transverse modulus of 700 
to 1200 lbs. or more. 



AKTIFICIAL STOMKiS.— FIRE-BRICK. 25 

Poor building brick will absorb from ^^ to J of their weight of 
water iu 24 hours, and average a little more than half the trans- 
verse* and crushing strength of good brick. 

An immersed brick is nearly saturated in the first hour of 
immersion ; in the remaining 24. hours the absorption is only 0.5 
to 0.8 per cent of its weight, as a rule. 

The strength of bricks in the kiln is least in the top courses, 
and increases quite rapidly for the first 10 or 12 courses and 
afterwards more slowly down to the arch bricks. 

Bricks made by the dry process are, as a rule, notably less 
porous and stronger than those made by the wet-mud process. To 
this rule, however, there are some exceptions. 

Effect of Fkost. — To ascertain if bricks will withstand the 
action of frost, boil one for half an hour in a solution of sulphate 
of soda, allow to remain in the solution until cold, then suspend it 
by a string over the vessel in which it has been boiled. In 24 
hours the surface of the brick will be covered with small crystals; 
the brick is then to be immersed in the solution until the crystals 
disappear, and again suspended. Repeat this operation for five 
days. If after this treatment a number of particles of brick are 
found at the bottom of the vessel, the bricks are incapable of re- 
sisting the effects of frost. 

Fire-brick. 

Fire-brick is used wherever high temperatures are to be resisted. 
They are made from fire-clay by processes very similar to those 
adopted in making ordinary brick, 

Fire- clay may be defined as native combinations of hydrated 
silicates of alumina, mechanically associated with silica and 
alumina in various states of subdivision, and sufficiently free 
from silicates of the alkalies and from iron and lime to resist 
vitrification at high temperatures. The presence of oxide of iron 
is very injurious; and, as a rule, the presence of 6 per cent justi- 
fies the rejection of the brick. The presence of 3 per cent of com- 
bined lime, soda, potash, and magnesia should be a cause for 
rejection. The sulphide of iron — pyrites — is even worse than 
the substances first named. 

A good fire-clay should contain from 52 to 80 per cent of silica 
and 18 to 35 per cent of alumina and have an uniform texture, 
a somewhat greasy feel, and be free from any of the alkaline 
earths. 



26 ARTIFICIAL STONES. — TERRA-COTTA. 

Good fire brick should be uniform in size, regular in shape, 
homogeneous in texture and composition, easily cut, strong, ^nd 
infusible. 

A properly burnt fire-brick is of an uniform color throughout its 
mass. A dark central patch and concentric rings of various shades 
of color is due mainly to the different states of oxidation of the 
iron and partly to the presence of unconsumed carbonaceous mat- 
ter, and indicates that the brick was burned too rapidly. 

Fire-brick are made in various forms to suit the required work. 
A straight brick measures 9 X 4| X 2^ inches and weighs about 7 
lbs., or 120 lbs. per cubic foot ; specific gravity 1.93. One cubic 
foot of wall requires 17 9-inch bricks ; one cubic yard requires 
460. One ton of fire-clay should be suflScientto lay 3000 ordinary 
bricks. 

English fire-bricks measure 9 X 4J X 2J inches. 

To secure the best results fire-brick should be laid in the same 
clay from which they are manufactured. It should be used as a 
thin paste, and not as mortar: the thinner the joint the better the 
furnace wall. The brick should be dipped in water as they are 
used, so that when laid they will not absorb the water from the 
clay paste. They should then receive a thin coating of the prepared 
fire-clay, and be carefully placed in position with as little of the 
fire-clay as possible. 

Terra-cotta. 

Terra-cotta is largely used as a substitute for stone in the 
ornamental part of buildings. It is composed of mixed clays, to 
which sometimes is added a large proportion of ground glass, 
pottery, and sand. After being properly kneaded it is forced into 
moulds smeared with soft soap; it is then carefully dried, and 
gradually baked in a pottery-kiln, and then slowly cooled. 

When properly prepared and burnt it is not affected by the 
atmosphere or acid fumes. 

Terra-cotta is subject to unequal shrinkage in baking, which 
sometimes causes the pieces to be twisted. When this is the case 
great care must be taken in laying the blocks; otherwise the long 
lines of a building, such as those of string-courses or cornices^ 
which are intended to be straight, are apt to be uneven, and the 
faces of the blocks are often in winding. 

Twisted and warped blocks are sometimes set right by chiselling, 
but this should be avoided, for if the vitrified skin on the surface 



I 



ARTIFICIAL STONES. — TERRA-COTTA. 27 

be removed the material will not be able to withstand the attacks 
of the atmosphere, etc. 

Terra- cotta is made in several colors, depending chiefly upon the 
amount of heat it has gone through. White, pale gray, pale 
yellow or straw color indicate a want of firing. Rich yellow, pink, 
and red varieties are generally well burned. A green hue is a 
sign of absorption of moisture and of bad material. 

Inferior terra-cotta is sometimes made by overlaying a coarsely 
prepared body with -a thin coating of a finer and more expensive 
clay Unless these bodies have been most carefully tested and 
assimilated in their contraction and expansion, they will in the 
course of time destroy one another; that is, the inequality in their 
shrinkage will cause hair-cracks in the outer skin, which will 
retain moisture, and cause the surface layer to fall off in scales 
after winter frosts. 

Another very reprehensible custom is that of coating over the 
clay, just before it goes into the kiln, with a thin film of some 
ochreish paint mixed with a finely ground clay, which produces a 
sort of artificial bloom which speedily wears off after exposure to 
the action of the atmosphere. 

Terra-cotta, whether plain or ornamental, is generally made of 
hollow blocks formed with webs inside, so as to give extra 
strength and keep it true while drying. This is necessitated 
because good, well- burned terra-cotta cannot safely be made of 
more than about 1^ inches in thickness, whereas when required 
to bond with brickwork it must be at least four inches thick. 
When extra strength is needed these hollow spaces are filled with 
concrete or brickwork, which greatly increases the crushing 
strength of the terra-cotta, although alone it is able to bear a very 
heavy weight. A solid block of terra-cotta of one foot cube has 
borne a crushing strain of 500 tons and over. 

Table 5. 

RESISTANCE TO CRUSHING OF TERRA-COTTA. 

Tons per 
Cubic Foot 

Solid block 523 

Hollow block (unfilled) 186 

" " (slightly made and unfilled) 80 

Solid " 2-inch square, red 492 

buff 449 

gray 369 



28 ARTIFICIAL STONES. — TILES. 

The safe working strength of unfilled blocks may be taken at 5 
tons per square foot, and for blocks filled solid with concrete or 
brickwork at 10 tons per square foot. 

The weight of terra-cotta in solid blocks is 122 pounds per 
cubic foot; the weight of hollow blocks 1^ inches thick varies 
from 65 to 85 pounds per cubic foot. Porous terra- cotta roofing 3 
inches thick weighs 16 pounds per square foot, and 2 inches thick 
12 pounds. 

Porous Terha-cotta is made of a mixture of clay and some 
combustible material, such as sawdust, charcoal, cut straw, etc. 
When baked the combustible material is consumed, leaving the 
terra-cotta full of small holes. It is fireproof, of light weight, 
great tenacity, strong, can be cut with edge-tools, will hold nails 
driven in, and gives a good surface for plastering. 



Tiles. 

Common Tiles are made of the same materials as bricks; they 
are used for paving and roofing. 

Encaustic Tiles are those in which the colors are produced by 
substances mixed with the clay. 

Paving Tiles are of many shapes and sizes, and about one 
inch thick. 

Roofing Tiles are of many forms and sections, such as plain, 
corrugated, Venetian, ridge, etc. 

Flat Tiles 6J" X 10|" X T weigh from. 15 co 18 lbs. per 
square foot of roof, the lap being one half the length of the tile. 
Tiles with grooves and fillets weigh from 7 to 9 lbs. per square 
foot of roof. 

Pan Tiles 14V' X 10^" laid 10" to the weather weigh about 8 
lbs. per square foot. 

Inspection of Tiles. 

The inspection and testing of tiles should embrace : 

1. Examination of dimension, appearance, and soundness. 

2. Weight and specific gravity. 

3. The real and apparent absorption of water. 

4. Presence of constituents soluble in water. 

5. Strength. . 



ARTIFICIAL STONES. 29 

Stones made by Patented Processes, 

Several kinds of artificial stone are manufactured under 
jiatented processes. They are all a combination of hydraulic 
cement, sand, pebbles, stone-dust, etc., with or without the addi- 
tion of some indurating material, as baryte, litharge, etc. They 
are manufactured either in place or in form of blocks at a factory. 
Such stones are extensively employed in architecture and for the 
paving of cellars, areas, footpaths, etc. 



30 LIME. 



IV. Cementing Materials. 

The cementing materials employed in building are produced by 
the calcination of calcareous minerals. As these minerals differ 
greatly in their composition, ranging from pure carbonate of lime 
to stones containing variable proportions of silica, alumina, mag- 
nesia, oxide of iron, manganese, etc., they confer different prop- 
erties upon the calcined product, which render necessary certain 
precautions in its manipulation and treatment, and furnishes a 
basis of classification, as follows : 

1st. Common or fat limes. 

2d. Poor or meagre limes. 

3d. Hydraulic limes. 

4th. Hydraulic cements, which may be divided into three 
classes, viz. : Portland, Rosendale, and Pozzuolana. The first 
two differ from the third in that the ingredients of which the 
former are composed must be roasted before they acquire the 
property of hardening under water, while the ingredients of the 
latter need only be pulverized and mixed with water to a paste. 

The hydraulic cements do not slake after calcination, differing 
materially in this particular from the limes proper. They can be 
formed into paste with water, without any sensible increase in 
volume, and little, if any, disengagement of heat, except in cer- 
tain instances among those varieties which contain the maxi- 
mum amount of lime. They do not shrink in hardening, like the 
mortar of rich lime, and can be used with or without the addition 
of sand, although for the sake of economy sand is combined 
with them. The hydraulic activity of some of them is so ener- 
getic as to set under water at 65° F= in three or four minutes, 
although others require as many hours. 

liimes. 

Rich Limes. — The common fat or rich limes are those obtained 
by calcining pure or very nearly pure carbonate of lime. In 
slaking they augment to from two to three and a half times that 
of the original mass. They will not harden under water, or even 
in damp places excluded from contact with the air. In the air 
they harden by the gradual formation of carbonate of lime, due 
to the absorption of carbonic acid gas. 



LIME. 31 

The pastes of fat lime shrink in hardening to such a degree 
that they cannot be employed for mortar without a large dose of 
sand. 

Poor Limes. — The poor or meagre limes generally contain 
silica, alumina, magnesia, oxide of iron, sometimes oxide of man- 
ganese, and in some cases traces of the alkalies, in relative pro- 
portions, which vary considerably in different localities. In 
slaking they proceed sluggishly, as compared with the rich limes 
— the action only commences after an interval of from a few 
minutes to more than an hour after they are wetted ; less water is 
required for the process, and it is attended with less heat and 
increase of volume than in the case of fat limes. 

Hydraulic Limes. — The hydraulic limes, including the three 
subdivisions of limes, viz., slightly JiydrauUCy hydraulic, and 
eminently hydraulic , are those containing after calcination suf- 
ficient of such foreign constituents as combine chemically with 
lime and water to confer an appreciable power of setting or hard- 
ening under water without the access of air. They slake still 
slower than the meagre limes, and with but a small augmentation 
of volume, rarely exceeding 30 per cent of the original bulk. 

Inspection of Liinie. 

Quality. — The quality of good lime is indicated by the per- 
fectness with which the lumps fall to powder when water is 
applied. No mashing of the lumps or stirring should be neces- 
sary, though the slaking will be somewhat hastened by so doing. 

Freshly turned lime may be known by its being in hard lumps 
rather than in powder or easily crumbled lumps. 

Preservation. — Lime, on account of its affinity for moisture, 
and, when moist, for carbonic acid, absorbs them gradually from 
the atmosphere, and returns somewhat to the state of carbonate 
of lime; this process is termed "air-slaking" and weakens the 
setting quality of the lime. To protect it from this deteriorat- 
ing action it should be packed in close casks and stored in a dry 
place until required for use, and then quickly used; therefore the 
best lime for use is that which has been recently burned. 

Lime, when thoroughly slaked and mixed into a paste, may be 
kept for an indefinite time in that condition without deterioration 
if protected from contact with the air so that it will not dry up. 
It is customary to keep the lime paste in casks, or in the wide 
shallow boxes in which it was slaked, or heaped up on the ground, 



32 LIME. 

covered over with the sand to be subsequently incorporated with 
it in making the mortar. 

Slaking. — Slaking is the process of chemical combination 
of quicklime with water ; one equivalent of water combines with 
one equivalent of lime, and forms slaked lime, or, in chemical lan- 
guage, hydrate of lime. 

The process of slaking is a simple one. The lime is spread out in 
a suitable bed and as much water as it will readily absorb is 
poured upon it. This moistening with water gives rise to various 
phenomena : the lime almost immediately cracks, swells, and falls 
into a bulky powder with a hissing, crackling sound, slight explo- 
sions, and considerable evolution of heat and steam ; the volume 
is increased from two to three and a half times the original bulk, 
the variation depending both upon the density of the original car- 
bonate and the manner of conducting the process. 

The same process takes place slowly by absorption of moisture 
from the atmosphere ; the lime falls into powder with increase 
of volume, but without perceptible heating. Lime slaked in 
this way is said to be air-slaked. Some carbonic acid gas is also 
absorbed and a part of the lime returns to the state of a carbonate 
of lime. 

Air-slaked lime is deficient in setting properties and should not 
be used for building purposes. 

The common limes contain impurities which prevent a thor- 
ough, uniform, and prompt slaking of the entire mass ; hence the 
necessity of slaking some days before the lime is required for use, 
to avoid all danger to the masonry by subsequent enlargement of 
volume and change of condition. 

The slaking of lime, although an exceedingly simple operation, 
is liable to be unskilfully performed by the workmen. They are 
apt either to use too much water, which reduces the slaked 
lime to a semi-fluid condition and thereby injures its binding 
qualities ; or, not having used enough water in the first place, 
seek to remedy the error by adding more after the slaking has 
well progressed and a portion of the lime is already reduced to 
powder, thus suddenly depressing the temperature and chilling 
the lime, which renders it granular and lumpy. The lime should 
not be stirred while slaking. The essential point is to secure the 
reduction of all the lumps. 

The best mode of slaking, so far as regards the quality of the 
mortar, is by sprinkling the loose lump lime with about one fourth 
to OHO third by trial of its own bulk of water, and then covering 



LIME. 33 

it with a layer of sand or with a tarpaulin ; this retains the heat 
and accelerates the slaking. All the lime necessary for any re- 
quired quantity of mortar should be slaked at least one day before 
it is incorporated with the sand. 

Memoranda and Definitions of Liime, 

Lime is shipped either in bulk or in barrels. If in bulk, it is 
impossible to preserve it for any considerable length of time. 

A barrel of lime usually weighs about 230 lbs. net, and will 
make about three tenths of a cubic yard of stiff paste. A bushel 
weighs 75 lbs. 

Pure Lime is a protoxide of calcium, or, in other words, a 
metallic oxide. It has a specific gravity of 2.8, is amorphous, 
somewhat spongy, highly caustic, quite infusible, possesses great 
affinity for water, and if brought in contact with it will rapidly 
absorb 22 to 23 per cent of its weight, passing into the cohdition 
of hydrate of lime. 

Slaked Lime is hydrate of lime. 

Quicklime, or caustic lime, is the resulting lime left from the 
calcination of limestone — it is chemically known as calcium oxide. 

Limestone. — Carbonate of lime. 

Crystallized Lime. — Marble. 

Fossil Lime. — Chalk. 

Sulphate of Lime. — Gypsum. 

Calcination is heating to redness in air. 

Slaking is the process of chemical combination of quicklime 
with water. 

Air-slaking. — Hydration by the absorption of moisture from 
the atmosphere. 



34 CEMENTS. 

Portland Cement. 

Portland cement is produced bj burning, with a heat of suf- 
ficient intensity and duration to induce incipient vitrification, 
certain argillaceous limestones, or calcareous clays, or an artificial 
mixture of carbonate of lime and clay, and then reducing the 
burnt material to powder by grinding. Fully 95 per cent of the 
Portland cement produced is artificial. The name is derived from 
the resemblance which hardened mortar made of it bears to a 
stone found in the isle of Portland, off the south coast of England. 

The quality of Portland cement depends upon the quality of the 
raw materials, their proportion in the mixture, the degree to 
which the mixture is burnt, the fineness to which it is ground, 
and the constant and scientific supervision of all the details of 
manufacture. 

Characteristics of Portland Cement. 

Color. — The color should be a dull bluish or greenish gray, 
caused by the dark ferruginous lime and the intensely green man- 
ganese salts. Any variation from this color indicates the presence 
of some impurity : blue indicates an excess of lime ; dark green, 
a large percentage of iron ; brown, an excess of clay ; a yellowish 
shade indicates an underburned material. 

Fineness. — It should have a clear almost floury feel in the hand; 
a gritty feel denotes coarse grinding. 

Weight. — It should weigh from 84 to 88 pounds per cubic foot. 
A cement weighing from 70 to 80 pounds per cubic foot is invari- 
ably a weak one, though it may be of the requisite fineness ; at 
the same time a heavy cement if coarsely ground is also weak and 
will have no carrying capacity for sand. Light weight may be 
caused by laudable fine grinding or by objectionable underburn- 
ing. In testing, weight and fineness must be taken in conjunction. 

Specific Gravity is between 3 and 3.05. As a rule the strength 
of Portland cement increases with its specific gravity. 

Tensile Strength. — When moulded neat into a briquette 
and placed in water for seven days it should be capable of resisting 
a tensile strain of from 300 to 500 pounds per square inch. 

Setting — A pat made with the minimum amount of water 
should set in not less than three hours, nor take more than six 
hours. 

Expansion and Contraction. — Pats left in the air or placed 
in water should during or after setting show neither expansion nnr 
contraction, either by the appearance of cracks or change of form. 



CEMEN^TS. 35 

A cement that possesses the foregoing properties may be con- 
sidered a fair sample of Portland cement and would be suitable 
for any class of work. 

OvERLiMED Cement is likely to gain strength very rapidly in 
the beginning and later to lose its strength, or if the percentage 
of free lime be sufficient it will ultimately disintegrate. 

Blowing or Swelling of Portland cement is caused by too 
much lime or insufficient burning. It also takes place when the 
cement is very fresh and has not had time to cool. 

Adulteration. — Portland cement is adulterated with slag 
cement and slaked lime. This adulteration may be distinguished 
by the light specific gravity of the cement, and by the color, which 
is of a mauve tint in powder, while the inside of a water-pat when 
broken is deep indigo. Gypsum or sulphate of lime is also used 
as an adulterant. 

Natural Cement. 

The Bosendale or natural cements are produced by burning in 
draw-kilns at a heat just sufficient in intensity and duration to 
expel the carbonic acid from argillaceous or silicious limestones 
containing less than 77 per cent of carbonate of lime, or argillo- 
magnesian limestone containing less than 77 per cent of both car- 
bonates, and then grinding the calcined product to a fine powder 
between millstones. 

The natural cements usually take the name of the place of 
manufacture. The name Rosendale is derived from the place (Ro- 
sendale, Ulster Go., N. Y.) where it was first made. 

Characteristics of Rosendale Cements. 

The natural cements have a porous, globular texture. They do 
not heat up nor swell sensibly when mixed with water. They set 
quickly in air, but harden slowly under water, without shrinking, 
and attain great strength with well-developed adhesive force. 

Color. — Usually brown, of greater or less intensity. The color 
gives no clue to the cementitious value, since it is due chiefly to 
oxides of iron and manganese, which bear no direct relation to the 
cementing properties. A very light color generally indicates an 
inferior underburned cement. A Rosendale cement made at Cop- 
lay, Pa., from the same stone as Portland is a light gray in color. 

Setting. — A pat made with the minimum amount of water 
should spt in nbout 30 ininntos. 



36 CEMENTS. 

Fineness. — At least 93 per cent must pass through a No. 50 
sieve. 

Weight.— Varies from 49 to 56 pounds per cubic foot. 

Specific Gravity about 2.70. 

Tensile Strength.— Neat cement one day, from 40 to 8il- 
pounds. Seven days, from 60 to 100 pounds. One year, from 
300 to 400 pounds. 

Inspection of Cement. 

The quality or constructive value of a cement is generally 
ascertained by submitting a sample of the particular cement to a 
series of tests. The properties usually examined are the color, 
weight, activity, soundness, fineness, and tensile strength. Chemical 
analysis is sometimes made, and specific gravity test is substituted 
for that of weight. Tests of compression and adhesion are also 
sometimes added. As these tests cannot be made upon the site of 
the work, it is usual to sample each lot of cement as it is delivered 
and send the samples to a testing laboratory. 

Sampling Cement. — The cement is sampled by taking a small 
quantity (1 to 2 lbs.) from the centre of the package. The num- 
ber of packages sampled in any given lot of cement will depend 
upon the character of the work, and varies from every package 
to 1 in 5 or 1 in 10. When the cement is brought in barrels th«? 
sample is obtained by boring with an auger either in the heaij 
or centre of the barrel, drawing out a sample, then closing the 
hole with a piece of tin firmly tacked over it. For drawing out 
the sample a brass tube sufificiently long to reach the bottom oC 
the barrel is used. This is thrust into the barrel, turned around^ 
pulled out, and the core of cement knocked out into the sample- 
can, which is usually a tin box with a tightly fitting cover. 

Each sample should be labelled, stating the number of the sam- 
ple, the number of bags or barrels it represents, the brand of 
the cement, the purpose for which it is to be used, the date of 
delivery, and date of sampling. 

Form op Label. 



Sample No 

No. of Barrels 

Brand 

To he used 

Delivered 18. . Sampled 18. 

By 



CEMEKTS. 37 

The sample should be sent at once to the testing office, and 
none of the cement should be used until the report of the tests is 
received. 

The testing of cement ordinarily consumes 30 days. Therefore 
the supply must be so gauged that a sufficient quantity will be 
kept on hand to allow the tests to be made without delay to the 
work of construction. 

After the report of the tests is received the rejected packages 
should be conspicuously marked with a "C" and should be re- 
moved without delay ; otherwise it is liable to be used. 

Rough Tests for Cement. — As one lot of cement is liable to 
differ very much from another lot of the same brand, it is very 
necessary that the inspector apply some rough tests to get an 
idea of how the cement is running. 

Test for Setting. — Make a small pat of neat cement and 
note the interval of time that elapses until it resists penetration 
under a light pressure of the thumb-nail. 

Test for Expansion. — Make a small pat of neat cement and 
when set in air place it under water, where it should remain for 
a few days. If the cement be good the pat will show no altera- 
tion in form, but if any cracks show on the edges, or other devia- 
tions from the original shape of the pat, they indicate that the 
cement is of an expansive nature, and therefore not to be trusted. 
But because a cement will not stand this test it is not in all cases 
to be condemned as useless, as its expansive or blowing property 
may be attributable to its being used too soon after leaving the 
mill. A proper process of cooling — placing it in a thin layer on a 
dry floor for a short time — may correct the defect. 

Test for Soundness. — Place some mortar of neat cement in a 
glass tube (a milled lamp-chimney is excellent for this purpose) 
and pour water on top. If the tube breaks the cement is unfit 
for use in damp places. 

Contraction due to the cement being overclayed may be ae- 
tected by a similar test to that for expansion. 

Ball Test. — This test is extensively employed by masons. 
Take enough neat cement to make a ball an inch in diameter, mix 
with just sufficient water to make it mould readily, and roll it into 
a ball. Allow it to set in air for about two hours, then place 
under water, and allow it to remain from 1 to 10 days. It should 
become gradually harder, and show no signs of cracking or crum- 
bling. Any cement that does not endure this test is not of suffi- 
ciently good quality to make satisfactory work. 



38 CEMENTS. 

Preservation of Cements. — Cements require to be stored in 
a dry place protected from the weather ; the packages should not 
be placed directly on the ground, but on boards raised a few 
inches from it. If necessary to stack it out of doors a platform 
of planks should first be made and the pile covered with canvas, 
Portland cement exposed to the atmosphere will absorb moisture 
until it is practically ruined. The absorption of moisture by the 
natural cements will cause the development of carbonate of lime, 
which will interfere with the subsequent hydration. 

Cements— Memoranda and Definitions. 

Cement is shipped in barrels or in cotton or paper bags. 
The usual dimensions of a barrel are : length 3 ft. 4 in. , middle 
diameter 1 ft. 4J in., end diameter 1 ft. 3| in. 
The bags hold 50, 100, or 200 pounds. 
A barrel weighs about as follows : 

Rosendale, N. Y 300 lbs. net 

*' Western 265 

Portland 375 

A barrel of Rosendale cement contains about 3.40 cubic feet 
and will make from 3.70 to 3.75 cubic feet of stiff paste, or 79 to 
83 pounds will make about one cubic foot of paste. A barrel of 
Rosendale cement (300 lbs.) and two barrels of sand (7^ cubic 
feet) mixed with about half a barrel of water will make about 8 
cubic feet of mortar, sufficient for 

192 square feet of mortar- joint i inch thick 
288 " •♦ " '' I "■ 

384 '* " •' *' i •' 

768 ** *' *• '' \ ** 

A barrel of Portland cement contains about 3.25 to 3.35 cubic 
feet — 100 pounds will make about one cubic foot of stiff paste. 

A barrel of cement measured loosely increases considerably in 
bulk. The following results were obtained by measuring in quan- 
tities of two cubic feet : 

1 bbl. Norton's Rosendale gave 4.37 cu. ft. 

*' Anchor Portland " 3.65 " 

Sphinx " " 3.71 

" Buckeye '* " 4.25 " 



CEMENTS. 39 

Tlie weight of cement per cubic foot is as follows , 

Portland, Englisli and German 77 to 90 lbs. 

•* fine-ground French 69 '* 

*' American 92 " 95 ** 

Rosendale 49 " 56 *' 

Roman 54 ** 

A bushel contains 1.244 cubic feet. The weight of a bushel can 
be obtained sufficiently close by adding 25^ to the weight per 
cubic foot. 

Activity denotes the speed with which a cement begins to 
iet^ Cements differ widely in their rate and manner of setting. 
Some occupy but a few minutes in the operation, and others 
require several. Some begin setting immediately and take con- 
siderable time to complete the set, while others stand for a con- 
siderable time with no apparent action and then set very quickly. 
The point at which the set is supposed to begin is wJien the 
stiffening of the mass first becomes perceptible, and the end of the 
Bet is when cohesion extends through the mass sufficiently to offer 
such resistance to any change of form as to cause rupture before 
any deformation can take place. 

Fineness. — The cementing and economic value of a cement is 
affected by the degree of fineness to which it is ground. Coarse 
particles in a cement have no setting power and act as an adul- 
terant. In a mortar or concrete composed of a certain quantity of 
inert material bound together by a cementing material it is evident 
that to secure a strong mortar or concrete it is essential that each 
piece of aggregate shall be entirely surrounded by the cementing 
material, so that no two pieces are in actual contact. Obviously, 
then, the finer a cement the greater surface will a given weight 
cover, and the more economy will there be in its use. 

The proper degree of fineness is reached when it becomes 
cheaper to use more cement in proportion to the aggregate than to 
pay the extra cost of additional grinding. 

The fineness of a cement is determined by measuring the per- 
centage which will not pass through sieves of a certain number of 
meshes per square inch. Three sieves are generally used, viz. : 

No. 50, 2,500 meshes per square inch 
** 74, 5,476 
" 100, 10.000 



40 CEMENTS. 



1 



^he usual degree of fineness required is that the residue left on 
a No. 50 sieve shall not be more than 10 per cent by weight. 

Freezing of Cement Mortaes. — Portland cement mortar 
suffers no surface disintegration under any condition of freezing, 
but the strength is impaired, in a majority of cases, and some- 
times as much as 40 per cent. 

Kosendale cement is disintegrated upon the surface when 
exposed to frost while setting, the amount of injury depending to 
a certain extent upon the number of degrees of the exposure 
below the freezing-point. 

The cohesion of Rosen dale cement mortar may be entirely 
destroyed by immersion in water, which becomes frozen around it. 

In some cases Rosendale cement shows an increase of strength 
acquired under the conditions which it passes through while 
frozen. 

Portland cement is injured relatively less by freezing as the 
ratio of cement to sand decreases. 

Salt used in the mixing water, in proportions varying around 1 to 
15, assists Rosendale cement to resist the disintegrating action of 
frost, but appears to have an injurious effect on the strength. 
The injury to Portland cement is decreased with about the same 
proportion of salt. 

Hydratjlicity. — Lime or cement is said to be more or less 
hydraulic according to the extent to which paste or mortar made 
from it will set under water, or in positions where it is excluded 
from the action of the air. 

Hydraulic Activity is the term used to denote the quickness 
or time required for a mortar to attain a small degree of strength. 

Hydraulic Energy or Strength is the term applied to the 
ultimate strength attained by a mortar. There is no necessary 
relation between time of setting and ultimate strength ; but, as 
a general rule, the slow-setting cements ultimately attain to a 
greater strength than quick- seting ones. 

Quick and Slow Setting. — The aluminous natural cements 
are commonly ** quick-setting," though not always so, as those 
containing a considerable percentage of sulphuric acid may set 
quite slowly. The magnesian and Portland varieties may be either 
** quick" or "slow." Specimens of either variety may be had 
that will set at any rate, from the slowest to the most rapid, and 
no distinction can be drawn between the various classes in this 
regard. 

Water containing sulphate of lime in solution retards the set 



CEMENTS. 41 

ting. This fact has been made use of in the adulteration of 
cement, powdered gypsum being mixed with it to make it slow- 
setting, greatly to the injury of the material. 

The temperature of the water used affects the time required for 
setting : the higher the temperature, within certain limits, the 
more rapid the set. Many cements which require several hours 
to set when mixed with water at a temperature of 40"* F. will 
set in a few minutes if the temperature of the water be increased 
to 80° F. Below a certain inferior limit, ordinarily from 30° to 
40° F., the cement will not set, while at a certain upper limit, in 
many cements between 100° and 140° F., a change is suddenly 
made from a very rapid to a very slow rate, which then contin- 
ually decreases as the temperature increases, until practically the 
cement will not set. 

The quick- setting cements usually set so that experimental 
samples can be handled within 5 to 30 minutes after mixing. The 
slow-setting cements require from 1 to 8 hours. Freshly ground 
cements set quicker than older ones. 

Strength. — The strength of a cement mortar is usually deter- 
mined by submitting a specimen of known cross-section to a 
tensile strain. The reason for adopting tensile tests is that com- 
paratively light strains produce rupture ; and that, since mortar is 
less strong in tension than in compression, in most cases of failure 
of mortar it is broken by tensile stress, even though the masonry 
be under compression. 

Table 6 shows the average minimum and maximum tensile 
strength per square inch which some good cements have attained. 

Setting denotes the process of combination amongst the par-" 
tides of the cement under the action of water. 

Soundness denotes the property of not expanding or contracting 
or cracking or checking in setting. These effects may be due to 
free lime, free magnesia, or to unknown causes. Testing sound- 
ness is, therefore, determining whether the cement contains any 
active impurity. An inert adulteration or impurity affects only its 
economic value; but an active impurity affects also its strength and 
durability. 



42 



CEMENTS. 



Table 6. 

TENSILE STRENGTH OF CEMENT MORTAR. 



Age of Mortar when Tested. 


Averag:e Tensile Strength in 
Pounds per Square Inch. 




Portland. 


Rosendale. 


Clear Cement. 
One hour, or until set, in air, the remain 
der of the time in water: 

1 day 


Min. 
100 

250 
350 
450 


Max. 
140 

550 
700 
800 


Min. 
40 

60 
100 
300 

30 

50 

200 


Max. 

80 


One day in air, the remainder of the time 
in water : 

1 iveek 


100 


4 wc€ks 


loO 


1 year 

1 Part Cement to 1 Part Sand. 
One day in air, the remainder of the time 
in water : 


400 
50 








80 








300 


1 Part Cement to 3 Parts Sand. 
One day in air, the remainder of the time 
in water : 

1 wesk 


80 
100 
200 


125 
200 
350 




4 weeks 






1 year 











Miscellaneous Cements. 

Slag Cements are those formed by an admixture of slaked lime 
witli ground blast-furnace slag. The slag used has approximately 
the composition of an hydraulic cement, being composed mainly 
of silica and alumina, and lacking a proper proportion of lime to 
render it active as a cement. In preparing the cement the slag 
upon coming from the furnace is plunged into water and reduced 
to a spongy form from which it may be readily ground. This is 
dried and ground to a fine powder. The powdered slag and 
fclaked lime are then mixed in proper proportions and ground 
together, so as to very thoroughly distribute them through the 
mixture. It is of the first importance in a slag cement that the 
slag be very finely ground, and that the ingredients be very uni- 
formly and intimately incorporated. 

Both the composition and methods of manufacture of slag 
cements vary considerably in different places. They usually con- 
tain a highar percentage of alumina than Portland cements, and 



CEMENTS. 43 

the materials are in a different state of combination, as, being 
mixed after the burning, the silicates and aluminates of lime 
formed during the burning of Portland cement cannot exist in slag 
cement. 

The tests for slag cement are that briquettes made of one part 
of cement and three parts of sand by weight shall stand a tensile 
strain of 140 pounds per square inch (one day in air and six in 
water), and must show continually increasing strength after seven 
days, one month, etc. At least 90 per cent must pass a sieve con- 
taining 40,000 meshes to the square inch, and must stand the 
boiling test. 

PozzuOLANAS are cements made by a mixture of volcanic ashes 
with lime, although the name is sometimes applied to mixed 
cements in general. The use of pozzuolana in Europe dates back 
to the time of the Romans. 

Roman Cement is a natural cement manufactured from the sep- 
taria nodules of the London Clay formation; it is quick-setting, 
but deteriorates by age and exposure to the air. 

Lafarge Cement. — This is a patented cement similar to Port- 
land, but, unlike Portland or the natural cements, does not stain 
marble, limestone, or other porous stones when used in setting 
them. For this reason it is largely used in setting and backing 
up the stone- work in fine buildings. 

Asphaltum* 

Bitumen? Asphaltum, K^t-km/t.— Bitumen is the name used 
to denote a group of mineral substances, composed of different 
hydrocarbons, found widely diffused throughout the world in a 
variety of forms which grade from thin volatile liquids to thick 
semi-fluids and solids, sometimes in a free or pure state, but more 
frequently intermixed with or saturating different kinds of in- 
organic or organic matter. 

To designate the condition under which bitumen is found dif- 
ferent names are employed ; thus the liquid varieties are 
known as naphtha and petroleum^ the semi-fluid or viscous as 
maltha or mineral tar, and the solid or compact as asphaltum or 
asphalt. 

Three distinct varieties of asphaltum are recognized, namely, 
the earthy, the elastic, and the hard or compact. 

The earthy variety, represented by the chapopota of Mexico, 
Colombia, and other parts of South America, has a brownish- 



44 CEMENTS. 

black dull color, an eartliy uneven fracture, when freslily exca- 
vated a strong though not unpleasant earthy odor, is soft enough 
to take an impression of the nail, hardens slightly on exposure to 
the atmosphere, and burns with a clear brisk flame, emitting a 
powerful odor, and depositing much soot. 

Elastic asphaltum is of various shades of brown; is soft, flexible, 
and elastic ; it has an odor strongly bituminous, and is of about 
the density of water ; it burns with a clear flame and much 
smoke. Like caoutchouc, it takes up pencil-marks, and on this 
account is called mineral caoutchouc; it has been found only at 
three places : in the fissures of a slaty clay ac Castleton, Eng- 
land ; at Montrelais, France ; and in Massachusetts. 

Hard or compact asphaltum is the most useful variety ; it forms 
large deposits in many parts of the world, and is of various de- 
grees of quality, according to its age and the impurities mixed 
with it ; when nearly pure its ordinary characteristics are as fol- 
lows : Color brownish black and black ; lustre resinous or coal-like ; 
opaque. At temperatures below 100° F. it is brittle and breaks 
with a conch oidal fracture. Melts ordinarily at 190° F. to 195° 
F., and is liquid at about 212° F. At 212° F. it has a peculiar 
but agreeable aromatic odor, somewhat resembling, but still very 
different from, that of coal-tar ; at ordinary temperatures the 
odor is scarcely perceptible, but when rubbed it is quite strong. 
It kindles readily and burns brightly with a thick smoke. Dis- 
tilled by itself it yields a bituminous oil of a yellow color (con- 
sisting of hydrocarbons mixed with oxidized matter), water, some 
combustible gases, and sometimes traces of ammonia. 

After combustion it leaves about one third of its weight of 
charcoal and ashes containing silica, alumina, oxide of iron, 
sometimes oxide of manganese, lime, and other inorganic and 
organic matter. Its composition and hardness are variable. 

Specific Gravity. — Pure bitumen has a density less than water ; 
but in consequence of the impurities mixed with it the specific 
gravity of asphaltum varies from 1.0 to 1.7. Sol ability : It is 
insoluble in water, partly or wholly soluble in chloroform and 
disulphide of carbon, partly or wholly in oil of turpentine and 
petroleum ether, and commonly partly in alcohol. 

By different solvents asphaltum may be decomposed into three 
distinct though complex substances which have been named by 
Boussingault and other chemists who have investigated it petro- 
lene, asphaltene, and retine. Nothing definite is known concern- 
ing these compounds or how their variable proportions and 



CEMENTS.. 45 

composition affect the quality of asphaltum. In tlie past they 
have received but little attention from chemists, due probably to 
the limited use of asphaltum ; but now, in vievr of its large and 
increasing employment for paving and other industrial purposes, 
their investigation offers a wide and undoubtedly profitable field 
for chemical research. 

The characteristics of these compounds, so far as known, are 
generally as follows : 

Petrolene is the compound which is considered to give the vis- 
cous or adhesive quality. It may be described as that portion of 
the bitumen which is soluble in petroleum ether. It is lighter 
than water, very combustible, and has a high boiling-point, pale- 
yellow color, and peculiar odor. On evaporating off the ether it 
remains as a resin with a brownish-black color, which dissolves 
readily in the volatile oils. Its composition is carbon, hydrogen, 
and sulphur. The amount present in an asphaltum is variable, 
ranging from 3 to 70 per cent of the weight of the asphaltum. 

Asphaltene is the compound which gives the hardness to as- 
phaltum. It contains the elements of petrolene, together with a 
quantity of oxygen, and probably arises from the oxidation of 
that compound. It is that portion of the bitumen which is insol- 
uble in ether. It is dissolved out by carbon disulphide, chloro- 
form, benzene, etc. Its color is a brilliant black ; density greater 
than water. It burns like resins in general, leaving a very 
abundant coke. Like petrolene, it is composed of carbon, hydro- 
gen, and oxygen, and the amount present in an asphaltum is as 
variable — ranging from 1 to about 60 per cent. 

Retine is dissolved out by alcohol (anhydrous) from that por- 
tion of the asphaltum which is unaffected by the solvents above 
mentioned. It is a yellow resin composed of carbon, hydrogen, 
and sulphur. What effect this compound has upon asphaltum is 
unknown. Some authorities claim that its presence is injurious. 

Origin of Bitumen. — The origin of bitumen is unknown. It 
Is supposed to be the ultimate product resulting from the de- 
struction under certain conditions of the organized remains of 
animals and vegetables, producing (1) naphtha, (2) petroleum, (3) 
maltha or mineral tar, (4) asphaltum. The whole of these sub- 
stances merge into each other by insensible degrees, so it that is 
impossible to say at what point maltha ends and asphaltum begins. 
Naplitlia, the first of the series, is in some localities found flow- 
ing out of the earth as a clear, limpid, and colorless liquid ; as 
such it is a mixture of hydrocarbons, some of which are very vol- 



46 ' CEMENTS, 

atile and evaporate on exposure. It takes up oxygen froniTue 
air, becomes brown and thick, and in tliis condition it is called 
petroleum. 

Tlie hardening of the bituminous fluids which have oozed out* 
or been exposed by other causes upon the surface of the earth 
seems, in most cases at least, to have resulted from the loss of 
the vaporizable portions, and also from a process of oxidation 
which consists, first, in a loss of hydrogen, and finally in the 
oxygenation or evaporation of the more volatile portions, which 
gradually transforms them into mineral tar or maltha, and, still 
later, into solid glossy asphaltum, of which gilsonitey icurtzilite, 
uintahite, etc., are examples. 

Occurrence and Distribution of Asphaltum. — Deposits 
of asphaltum are found widely diffused throughout the world, 
and at various altitudes ranging from below sea-level to thou.^ 
sands of feet above. It is, however, seldom found among the 
primitive or older rock formations, but seems to belong exclu- 
sively to the secondary and tertiary formations. Intermixed with 
the argillaceous stratas it forms extensive beds or lake-like depos- 
its on both continents, the most remarkable of which are those 
situated in the West Indies and South America. The most nota< 
ble of these are the so-called pitch lakes on the island of Trini 
dad, and at Bermudez, Venezuela. 

Saturating the calcareous and sandstone formations, it forms 
large subterraneous deposits in Europe and the United States. 
The calcareous varieties occur more extensively in Europe than 
in America, and are the source of the material employod there for 
street-paving under the name of asphalie. The sandstone class 
is found extensively in the Western and Southwestern States, 
especially in California, Texas, Kentucky, and the Indian Ter- 
ritory. 

In a free or nearly pure state it is found in veins and seams in 
the primitive rock and volcanic formations. This class of deposit 
is rare, and the amount of asphaltum is generally insignificant. 
A notable exception, however, are the deposits of Utah, etc The 
mines from which gilsonite, wurtzilite, uintahite are produced are 
said to be very extensive, and the material is very nearly pure 
Similar deposits are found in Mexico, Cuba, and various parts of 
South America. 

In many localities beds of shale, sand, and cretaceous limestone 
are found saturated with maltha, from which the bitumen is 
extracted by boiling or macerating with water. 



I 



CEMENTS. 



47 



From the variety of the deposits and their manner of occurrence 
it seems that asphaltum belongs to no particular era or age. 
Moreover, the asphaltum obtained from these different sources is 
not uniform either in character, appearance, hardness, or chemical 
composition. The ultimate composition of specimens from several 
localities is given in the following table: 

COMPOSITION OF ASPHALTUM. 



Locality. 



Trinidad, W. I. ... 

Cuba, *' .... 

Caxatambo, Peru . 
N. S. (albertite) ... 
W. Va (grahamite) 
Auvergne, France. 

Oklahoma, I. T. . . . 

Mexico 

Utah (gilsonite) . . . 



Car- 
bon. 


Hydro- 
gen. 


(80.32 
■I to 
(85.89 
82.34 


6.30 

to 

11.06 

9.10 


88.66 
86.04 
76.45 
77.64 


9.69 
8.96 

7.83 
7.86 


1 55.00 

80.34 
80.88 


10.21 


10.09 
9.76 



Oxy- 
gen. 



0.56 

to 

1.40 

6.25 



Nitro- 
gen. 



to 
0.50 
1.91 



1.97 
13.14 

8.35 

7.14 

9.57 
6.05 



1.65 



2.93 



1.02 
2.74 



3.30 



Sul- 
phur. 



2.49 
to 

11.48 



trace 



Ash. 



0.40 



0.10 

2.26 

5.13 

24.91 

and silicates 



0.01 



Nomenclature — As indicated above, the varieties of bitumen 
and asphaltum are as numerous as the localities producing 
them ; hence there is a great variety of names used to designate 
the same substance, which is oftentimes misleading, if not con- 
fusing. As an illustration of this variety the following may be 
mentioned: native pitch, mineral pitch, glance pitch, grahamite, 
albertite, piauzite, elaterite, gilsonite, wurtzilite, uintahite, tur- 
rellite, etc. 

Sometimes the name of the locality where it is found is used as 
a prefix, and is thus useful to indicate the source. Such names 
are Dead Sea bitumen, Egyptian asphalt, Cuban, Trinidad, Ber- 
muda, Calif ornian, Kentucky, etc. 

The name asphalte has been adopted by the French to designate 
the material obtained from their bituminous limestone deposits, 
and is now generally employed throughout Europe to denote both 
the carbonate of lime impregnated with asphaltum and the pave- 
ment made from that material. 

The name UtJiocarhon has been adopted to designate a cretaceous 
limestone saturated with bitumen found in Texas. 

Some authorities apply the terms asphaltum, asphalt, and liquid 
asphalt to the semi-fluid and viscous bituminous substance, or 
maltha, which by heat may be transformed into asphaltum. This 



48 CEMENTS. 

application seems to be erroneous, because asplialtum technically 
means bitumen in the solid form. Others use the same terms to 
designate the entire mixture of bitumen, mineral and organic 
matter, while others apply them to denote the purified material. 

The names which seem to be the most used in the United States, 
and which are at the same time descriptive of the various classes, 
are as follows: 

Crude asphaltum or crude asphalt is applied to all mixtures of 
bitumen, clay, sand, etc.; e. g., crude Trinidad asphalt. 

Befined asphaltum or asphalt is used to denote the asphaltum 
after it has been wholly or partly freed from the combined organic 
and inorganic matters. 

The limestone rocks impregnated with bitumen are called 
bituminous or asphaltic limestones. The term rock asphalt is also 
applied to the same material, the name of the source being also 
used, as "Italian rock asphalt,'' *' Val de Travers rock asphalt,** 
etc. 

The sandstones containing bitumen are known as bituminous or 
asphaltic sandstones, the name of the source being also mentioned. 

The semi-fluid bitumen is designated by the names maltha and 
mineral tar. 

The term asphalt is also frequently but erroneously applied to 
various preparations in which the cementing material is coal-tar 
or the residue of oil-refineries, etc. — substances which are entirely 
dissimilar to asphaltum, though apparently possessing some of its 
characteristics. 

The term bitumen is employed to designate the truly bituminous 
portion of the asphaltum and its compounds. 

Refined Asphaltum is asphaltum freed from the combined 
water and accompanying inorganic and organic matter. By com- 
paratively simple operations the several varieties of asphaltum 
may be reduced to an equal state of purity. 

The argillaceous varieties, such as Trinidad, Bermudez, etc., are 
purified in iron vessels by the application of heat either directly 
from fire or indirectly by steam; the temperature employed ranges 
from 212° F. to 350° F. During the application of the heat the as- 
phaltum is liquefied, the combined water is evaporated, the organic 
matters rise to the surface and are skimmed off, and the inorganic 
settle to the bottom of the vessel; when the liberation of the im- 
purities is completed the liquid asphaltum is drawn off into 
barrels, and constitutes the refined asphaltum of commerce. 

The calcareous and silicious varieties are purified by boiling or 



CEMENTS. 49 

macerating them with hot water, according to the freedom with 
which they part with the intermixed impurities. During the 
action of the water the sand and other ingredients fall to the 
bottom of the vessel, and the bitumen rises to the surface or forms 
clots on the sides of the boiler, whence it is skimmed off and 
thrown into another boiler, where it is boiled for some time, 
during which the water and more volatile oils are evaporated, and 
the mineral matters still retained fall to the bottom, leaving the 
bitumen in the form of a thick viscid substance, in which state it 
is used in several of the arts. By continuing the boiling for a 
considerable time or by increasing the temperature to about 250° 
F. the volatile portions are driven off, and the viscid bitumen is 
brought to a condition which upon cooling causes it to become 
solid. 

The operation of refining or purifying, while exceedingly 
simple, requires to be performed with much care, for the reason 
that if the asphaltum is melted at too high a temperature it will 
be burned or coked, or if the heating is prolonged at a low tem- 
perature the result will be 'practically the same. In either case 
the petrolene is converted into asphaltene. 

Asphaltic Cement. — Asphaltum in a refined or pure state is 
valueless as a cementing medium, owing to its hardness, brittle- 
ness, and lack of cementitious properties; therefore it is necessary 
to add some substance which will impart to it the required plastic, 
adhesive, and tenacious qualities. This substance must be one 
that will partially dissolve the asphaltene and form a chemical 
union by solution instead of a mechanical mixture. The duty 
which it has to perform is an important and peculiar one : if it is 
a perfect solvent of the constituents of the bitumen the adhesive 
qualities will be destroyed; if it is an imperfect one the asphaltum 
will retain its brittleness. 

The requirements of a suitable flux are that it shall be a fluid 
containing no substances volatile under 300° F., and shall possess 
the power to dissolve the asphaltum without destroying or lessen- 
ing its adhesive properties. 

The materials employed to give the required qualities to the 
hard asphaltum are called the '* flux," and those in general use 
are crude or specially prepared residuum oil obtained from the 
distillation of petroleum, and crude or refined maltha. 

The process of adding the flux is called ** oiling 'or ** temper- 
ing," and is conducted as follows: The refined asphaltum is 
melted and the temperature raised to about 300° F. ; the oil 



50 CEMENTS. 

previously heated is then pumped or in other ways added to the 
asphaltum, in the proportion of 10 to 20 pounds of oil to 100 
pounds of refined asphaltum; the proportion of the oil is varied 
between the limits stated according to its quality, the hardness of 
the asphaltum, and the purpose for which the cement is to be em- 
ployed. The mixture of residuum oil and asphaltum is agitated 
either by mechanical means or by a blast of air for several hours 
or until the material has acquired the desired properties. The 
agitation must be performed with great thoroughness to secure a 
uniform mixture, and must be continued whenever the material 
is in a melted condition, as a certain amount of separation takes 
place when the melted cement stands at rest. It is therefore 
customary to agitate it constantly when in use as well as during 
its preparation. 

The process of " tempering " when maltha is used as the flux is 
practically the same as outlined above, with the exception that the 
mixing is performed at a lower temperature and entirely by 
mechanical means, and a separation of the ingredients seldom 
occurs when the cement is standing at rest. 

The maltha from many localities is to be had in the market ; it 
is sold for fluxing purposes under various trade names, among 
which may be named " Alcatraz " liquid asphaltum, ** Standard " 
liquid asphalt, ''Utah" liquid asphalt, etc.; also artificial flux- 
ing materials which are offered as substitutes for oil and maltha, 
such as the ''Pittsburg," asphaltic flux etc. The analyses of 
some of these fluxing agents are as follows : 

* Alcatraz " Liquid Asphalt. 

Specific gravity 1.05 

Bitumen soluble in carbon disulphide 98.70 percent 

Bitumen soluble in petroleum naphtha. ... 89.17 ** ** 

Mineral matter 1.30 ** *' 

Organic non-bituminous matter trace 

*' Utah " Liquid Asphalt (Crude). 

Specific gravity 0.9068 

Bitumen soluble in carbon disulphide 76 15 per cent 

Bitumen soluble in ether 64.90 " *' 

Mineral matter 3.40 " ** 

Organic non-bituminous matter 20.45 ' ' ** 

Loss at 100° C 24.72 '* " 



CEMENTS. 51 

"Pittsburg" Asphaltic Flux. 

Moisture 0.05 per cent 

Volatile oil 212" F. to 312° F 1.60 

Volatile oil about 312° F 89.19 

Fixed carbon 8.48 

Ash 0. 68 

Bitumen soluble in carbon disulpliide 99.32 

Bitumen soluble in ether 65.00 

The enduring qualities of an asphaltic cement depend upon (1) 
the character of the fluxing agent, (2) the temperature at which 
the asphaltum has been refined, and the temperature at which the 
flax is added, (3) the degree of incorporation of the flux with the 
asphaltum, that is, whether the union is a chemical or mechanical 
one. 

Residuum Oil is a thick heavy oil varying considerably in 
;omposition, according to the source of the petroleum and method 
of distillation ; its base is par afflne — a substance so different from 
\A.sphaltum that when the two are brought together the result is a 
mixture partly mechanical and partly chemical, and, being of 
different specific gravities, they partly separate when allowed to 
.stand for any considerable period without stirring. 

In preparing the oil the object aimed at is (1) the removal of 
the hard paraflSnes, which are very susceptible to changes of tem- 
perature, becoming soft under the summer sun and brittle at or 
below the freezing-point; their presence imparts similar properties 
to the asphalt cement ; (2) to remove the lighter and more volatile 
oils ; care^in their removal must be exercised : if t^ o large a per- 
centage is removed the oil becomes heavy and thick, and too 
large a proportion is required to make a cement of suitable con- 
sistency — therefore there is a limit to the amount that can be 
removed. 

The oil is carefully examined to ascertain ; 

1. Specific gravity. 

2. Flash-point. 

3. Percentage volatile in a given time at 400° F. 

4 Susceptibility to changes of temperature as revealed by 
changes in viscosity. 

5. Presence of crystals of paraffine. 

The specifications of Washington, D. C, provide that the 
heavy petroleum oil used in the manufacture of asphalt cement 
shall have the following characteristics ; 



52 CEMEKTS. 

It sliall be a petroleum from wliicli tlie ligliter oils have been 
removed by distillation without cracking. 

Specific gravity Baume 17° to 21°. Flash-point not less than 
300° F. Distillate at 400° F. for ten hours less than 10 per cent. 

Shall not cease to flow above 60° F. Shall not require more 
than 21 pounds of oil for each 100 pounds of refined asphalt to 
produce the specific quality of cement. 

The flash-point shall be taken in a New York State closed oil- 
tester. The distillate shall be made with about 90 grams of oil in 
a small glass retort provided with a thermometer and packed en- 
tirely in asbestos. 

The flowing-point shall be determined by cooling 100 cc. of oil 
in a small bottle and noting the temperature at which it flows 
readily from one end of the bottle to the other. 

Analysis and Tests of Asphaltum. — The tests employed to 
determine the relative merits of asphaltum and asphaltic cements 
comprise both chemical and physical investigations. 

The chemical examination of the crude material involves the 
following determinations : 

Specific gravity. 
Percentage of moisture. 

** *• matter soluble in turpentine. 

*• ** ** ** '* carbon bisulphide, 

" •* *' ** •' alcohol. 

«* '• ** ** ** ether. 

" ** " volatile in 10 hours at 400° F. / 

•* ** sulphuretted hydrogen evolved at 400" F. 

•* ** non- bituminous organic matter. 

" " mineral constituents. 

. Softening-point. 

Flowing-point. 

The examination of the physical properties (mechanical tests) 
involves the following determinations : 

1. The refining of the crude material and making of an asphal- 
tic cement. 

2. Determining the penetrability of the cement. 

3 Making a paving mixture and testing it for tensile and 
crushing strength. 

The penetration tests are usually conducted in a machine in- 
vented by Prof. Bowen. This machine consists of a lever about 
17 inches long, having the fulcrum at one end and a cambric 



CEMENTS. 53 

needle inserted in the other end, above which is placed a weight 
of 100 grams. The end near the needle is connected by a steel 
rod and waxed cord with a spindle having a long hand which 
moves about a dial divided into 360 degrees. Another cord and 
weight upon an enlarged part of the spindle keeps the first- 
mentioned cord taut. By a suitably contrived spring clip the 
steel rod can be released for any length of time, and the needle, 
which has first been brought to coincide with the surface of the 
asphalt cement placed under it in a tin box, allowed to penetrate 
under the action of the weight into the cement. The number of 
degrees through which the hand moves on the dial records the 
penetration of the cement ; the length of time for which the 
needle is released is one second. Originally Prof. Bowen selected 
77° F. as the proper temperature at which the test should be 
made, and brought the cement and machine to this degree by 
keeping them in a room warmed to this point. But as it is some- 
times inconvenient or impossible to have a room temperature of 
77°, other temperatures may be made available by placing the tin 
sample-box of asphalt cement in water at 77° and allowing it to 
acquire that temperature, when the test can be made as before, 
certain allowance being made to reduce the result to the normal 
temperature of 77° F. 

The physical tests are performed in the usual machines em- 
ployed for testing other cements. 

^ s asphalt cement possesses the same qualities and can be used 
for the same purposes as hydraulic and other cements, its physi- 
cal qualities can be tested in a similar manner ; but the tests which 
have been made and published have been conducted without 
any regard to uniformity and under widely different conditions ; 
therefore they are of little or no value in determining the relative 
merits of the cements. 

Test for Bituminous Rock. — A specimen of the rock, freed 
from all extraneous matter, having been pulverized as finely as 
possible, should be dissolved in sulphurate of carbon, turpentine, 
ether, or benzine, placed in a glass vessel and stirred with a glass 
rod. A dark solution will result, from which will be precipitated 
the limestone. The solution of bitumen should then be poured 
off. The dissolvent speedily evaporates, leaving the constituent 
parts of the bitumen, each of which should be weighed so as to 
determine the exact proportion. The bitumen should be heated 
in & lead bath and tested with a porcelain or Baume thermometer 
to 428 degrees Fahr. There will be little loss by evaporation if 



54 CEMEKTS. 

tlie bitumen is good, but if bituminous oil is present tlie loss will 
be considerable. Gritted mastic should be heated to 450 degrees 
Fahr. The limestone should be next examined. If the powder 
is white and soft to the touch it is a good component part of 
asphalt i but if rough and dirty on being tested with reagents it 
will be found to contain iron pyrites, silicates, clay, etc. Some 
bituminous rocks are of a spongy or hygrometrical nature ; thus, 
as an analysis which merely gives so much bitumen and so much 
limestone may mislead, it is necessary to know the quality of the 
limestone and of the bitumen. 

The European bituminous limestone appears like a fine-grained 
rock, friable in summer, hard in winter. When heated to 50 or 
60 degrees centigrade it can be crushed between the fingers, 
and if exposed for several hours to a fierce sun it crumbles into 
unctuous brown powder. Examined under the microscope it is 
found to consist of minute calcareous grains, each covered with a 
thin film of bitumen, which causes them to adhere together. If 
a small portion is heated the cementing bitumen is melted and 
releases the solid particles from a loose heap of a deep chocolate 
color. If this powder is raised to 175 or 212 degrees Fahr. and 
rapidly compressed in a mould it will regain, in cooling, its 
original consistency in the new form. And the process may be 
indefinitely repeated, no change being produced by melting, fol- 
lowed by compression and cooling. 



TIMBER. 55 

V. TIMBER. 

Structure of Timber. 

Woods suitable for structural purposes are usually called tim- 
ber, and are almost exclusively obtained from trees that grow by 
the formation of layers of wood over the external surface, and 
therefore called exogenous. There are a few exceptions, as the 
trees of the palm family, the bamboo, etc., which belong to the 
endogenous class. 

When a tree is cut across it is seen that it is composed of three 

parts : 

1st. The hark, having a thickness of from J to IJ inches or 
more. This has no value for structural purposes, though useful 
in other respects ; it hastens the decay of the tree after felling, 
and should always be removed. 2d. The sap-wood, which lies 
next the bark, having a thickness varying from i to 4 inches ; 
it is indicated by a lighter color, by being softer and less com- 
pact than the inner portion. 3d. The central portion surrounded 
by the sap-wood and called the heart. The boundary between 
the sap-wood and the heart is in general distinctly marked. The 
heart-wood alone should be employed in those works in which 
strength and durability are required. Although the sap-wood is 
liable to rapid decay when exposed to unfavorable conditions, 
yet it can be safely used when entirely immersed in water, or 
when impregnated with certain preserving solutions, or when 
carefully seasoned and painted. 

Timber for building purposes may be divided into two classes : 
soft and hard. To the first class belong the pines and firs, to the 
second the oaks, chestnut, locust, hickory, etc. 

Properties of Timber.— Table 7 shows the weight and 
strength of timber collected from the experiments of different 
authorities. It will be seen that the figures vary throughout a 
very wide range, the difference being caused by the variations 
in the conditions of the growth of the timber, seasoning and pres- 
erveration, and upon the part of the tree from which the speci- 
men was cut, as well as upon the size and form of the piece tested 
and the method by which the test was applied. 

In taking figures from the table the lowest recorded should be 
taken, applying a large factor of safety to cover defects in the 
pieces used, which defects may not have e.iisted in the specimens 
experimented upon. 



56 



TIMBER. 



Table 7. 
DESCRIPTION AND PROPERTIES OF TIMBER. 



Description of Timber. 



I 



Weight 
per 
Cubic 
Foot 
Dry 
Lbs. 



Resistance to 



Ten- Crush- 
siou. ing. 



Cross- 
break- 
ing. 



Shearing. 



With 

the 

Grain. 



Aross 

the 

Grain. 



Pounds per Square Inch. 



Ash (White) 

C;olor brown ; sap- 
wood ruuch lighter, often 
nearly white. Wood 
heavy, hard, strong, ulti- 
mately brittle, coarse- 
grained, compact. Use: 
Interior and cabinet 
work. 



Ash (Red) 

Color rich brown; sap- 
wood light brown streak- 
ed with yellow. Wood 
heavy, strong, brittle, 
coarse-grained, compact. 
Use : As a substitute for 
the more valuable white 
ash, with which it is 
often confounded ..... 



Ash (Green) 

Colorbrown; sap-wood 
lighter. Heavy, hard, 
strong, brittle, coarse- 
grained. Use : Substitute 
for white ash 



Cedar (White) 

Color light brown, turn 
ing daiker with expo- 
sure; the thin sap-wood 
nearly white. Wood very 
light, soft, rather coarse- 
grai!ied. Very durable 
in contact with the soil. 
Used for posts, fencing, 
railway ties, and shin- 
gles. 



Cedar (Red) 

Color dull brown ting- 
ed with red; the thin sap- 
wood nearly white. Wood 
very light, soft, britile, 
rather coarse-giained. 
compact, easily worked. 
Very durable in contact 
with the soil. Used for 
interior finish, fencing, 
shingles. 



40.- 



38.96 



44.35 



19.72 

to 

20.70 



23.66 



g 






s 


S 


g 


o 


o 


s 






s 
-"s* 














«o 


CO 




o 


o 










i- 






o 


C 




-tJ 






1 


i 











TIMBER. 57 

DESCRIPTION AND PROPERTIES OF TIMBER. (Continued,) 



Description of Timber. 



Cedar (Central America). 



Weight 
per 
Cubic 
Foot 
Dry. 
Lbs. 



Cypress (Yellow) 

Color bright, light 
clear yellow ; sap-wood 
nearly white. Wood light, 
hard, brittle, close-grain- 
ed. Durable in contact 
with the soil. Easily 
worked. Satiny, polishes 
well. Has an agreeable 
resinous odor. Use 
Interior finish, cabinet 
work. 



Elm (White) 

Color light clear 
brown, often tinged with 
red ; sap-wood much 
lighter. Heavy, hard, 
strong, tough, very close- 
grained. Susceptible of 
polish. Use : Bridge tim- 
bers, sills, ties. 



Gum 

Color bright brown 
tinged, with red. Heavy, 
hard, tough, close-grain- 
ed, compact. Inclined 
to shrink and warp badly 
in seasoning. Suscepti- 
ble of a beautiful polish, 
Use : Boards and clap- 
boards, and as a substi- 
tute for black walnut. 



Hickory 

Color brown ; the thin 
and more valuable sap- 
wood nearly white. 
Wood heavy, very hard 
and strong, tough, close- 
grained, compact, flexi- 
ble. Use : Handles for 
implements, etc. 

Hemlock 

N. and S. Atlantic. . . . 

Pacific 

Color light brown ting- 
ed with red, or often 
nearly white. Sapwood 
somewhat darker. Wood 
light, soft, not strong, 



29.80 



45.26 



Resistance to 



Ten- 
sion. 



Crush- 
ing. 



Cross- 
break- 
ing. 



Shearing. 



With 

the 

Grain. 



Across 

the 
Grain. 



Pounds per Square Inch. 



ss% 



o 
8 



46.16 

to 

52.17 



26.42 
32.29 





B 












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58 



TIMBER. 



DESCRIPTION AND PROPERTIES OF TIMBER. (Continued.) 



Description of Timber. 



Weight 
per 

Cubic 
Foot 
Dry. 
Lbs. 



Resistance to 



Ten- 
sion. 



Crush- 
ing. 



Cross- 
break- 
ing. 



Shearing. 



With 

the 

Grain. 



Across 

the 
Grain. 



Pounds per Square Inch. 



brittle, coarse, crooked- 
grained. Difficult to 
work. Liable to wind 
shake and splinter. Not 
durable. Use : Rough 
lumber for construction 
Two varieties of the 
northern are recognized, 
red and white. 

Locust 

Color brown, or more 
rarely light green; sap 
wood yellow. Heavy, 
hard, strong, close-grain 
ed, compact. Very dur- 
able in contact with the 
ground. Use : Posts, 
turning. 

Lignum Vit^ 

Color rich yellow 
brown, varying to al 
most black ; sap-wood 
light yellow. Heavy, 
hard, strong, brittle, 
close-grained, compact. 
Difficult to work, splits 
irregularly. Use: Sheaves 
of blocks. 

Maple (Hard) 

Color light brown 
tinged with red ; sap- 
wood lighter. Heavy, 
hard, strong, tough, close- 
grained, compact. Sus- 
ceptible of a good polish. 
Use : Flooring, interior 
finish. 

Maple (White) 

Light, hard, strong, 
brittle, close-grained, 
compact. Easily worked 
Use: Flooring, furniture] 

Mahogany (Cent. America. 
Color red -brown of 
various shades and de- 
grees of brightness. Of- 
ten very much variedand 
mottled. Inferior qual' 
ties contain a large num- 
ber of gray specks. 
Wood strong, durable, 
flexible when green, brit- 
tle when dry, is very free 



45.70 



71.24 
to 

83.00 



43.08 



32.84 



35.00 



isi 



8 












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TIMBER. 



59 



DESCRIPTION AND PROPERTIES OF TIMBER. (Continued.) 



Description of Timber. 



from shakes; is seldom 
attacked by dry rot or 
worms. Requires care in 
seasoning ; i f seasoned too 
rapidly is liable to split 
into deep shakes. Use : 
Interior finish, handrails, 
patterns, etc. 
Oak (White) 

Color brown; sap-wood 
light brown. Wood 
heavy, strong, hard, 
tough, close-g rained! 
Checks if not carefully 
seasoned. Use : Interior 
finish, cabinet-making. 
Oak (Chestnut) 

Color dark brown; sap- 
wood much lighter. Wood 
heavy, hard , s tr ong, close 
grained. Checks badly in 
drying. Durable in con- 
tact with the soil. Use : 
Railroad ties. 
Oak (Live) 

Color light brown or 
yellow; sap-wood nearly 
white. Wood very heavy, 
hard, strong, tough, close- 
grained, compact. Diffl_ 
cult to work. Polishes. 
Oak (Red and Black) . 

Color light brown or 
red. Heavy, hard, coarse 
grained . Checks in dry. 
ing. Use : Interior finish 
and furniture. 
Palmetto (Florida) 

Color light brown 
Wood light, soft, fibres 
dark-colored. Hard and 
difficult to work. Use : 
Piles. Is impervious to 
the attacks of the Teredo^ 
and very durable under 
water. 

Pine (White) 

Color lightbrown, often 
slightl}^ tinged with red; 
sap-wood nearly white. 
Wood light, soft, very 
close, straight-grained. 
Easily worked. Polishes. 



Weight 
per 
Cubic 
Foot 
Dry. 
Lbs. 



46.35 



53.63 



59.21 



40.75 



27.44 



Resistance to 



Ten- 
sion. 



Crush- 
ing. 



Cross- 
break- 
ing. 



Shearing. 



With 

the 

Grain. 



Across 

the 
Grain. 



Pounds per Square Inch. 



SBw 



- 










CD 


s 


s 


B 


TJ« 






8000 

to 

10,000 


s 




i 


i 




B 


s 

00 




1 






O 


o 


o 


1 


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60 



TIMBER. 



DESCRIPTION AND PROPERTIES OF TIMBER. (Continued.) 



Description of Timber. 



Weight 

per 

Cubic 

I Foot 

Dry. 

Lbs. 



Resistance to 



Ten- 
sion. 



! Crush- 
1 ing. 



Cross- 
break- 
ing. 



Shearing. 



With 

the 

Grain. 



Across 

the 
Grain. 



Pounds per Square Inch. 



Use : Interior finish, win- 
dows, doors, etc 
Can., N. Atlantic States. 

N. Pacific coast 

I California 

Colorado 

Arizona 

Pine (Red), Norway Pine. 
Color light red; sap- 
wood yellow or white. 
Wood light, hard, coarse- 
grained, compact. Res- 
in-passages few, not 
conspicuous. Use : All 
purposes of construction . 

Pine (YeWow), Long-lea fed 
Color light red or 
orange: sap-wood nearly 
white. Wood heavy, hard, 
strong, tough, coarse, 
grained; compact. Dur- 
able. Cells resinous and 
dark-colored. Use : All 
purposes of construction. 

Pine (Yellow), Short-leafed 
Color orange ; sap-wood 
white. Wood varying 
greatly in quality and 
amount of sap. Heavy, 
hard , coarse-g rained, 
com pact. Cells broad, very 
resinous ; resin-passages 
numerous, large. Medul- 
lary rays numerous. Use: 
All purposes of construc- 
tion. Frequently substi- 
tuted for long - leafed 
pine, which is superior. 

Pine (Oregori)(Douglas Fir) 
Color varying from 
light red to yellow; sap- 
wood nearly white. Wood 
hard, strong, varying 
greatly with age, condi- 
tions of growth, and 
amount of sap. Difficult 
to work. Durable. Use : 
All kinds of construction. 
Two varieties, red and 
yellow; red considered 
less valuable than yellow. 



24.02 
24.35 
22.00 
27.00 
30.39 

30.25 



43.62 



38.40 



32.14 





















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o 






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TIMBER. 



61 



DESCRIPTION AND PROPERTIES OF TIMBER. (Continued.) 



Description of Timber. 



Weight 

per 
Cubic 
Foot 
Dry. 
Lbs. 



Poplar (Whitewood). . . . 
Color light yellow or 
brown; sapwood nearly 
white. Soft, brittle, very 
close, straight-grained, 
compact. Easily worked 
Use : interior finish, shin 
gles. 

Redwood (Pacific coast).. . 
Color clear, light red; 
Sap-wood nearly white, 
Wood light, soft, very 
brittle, coarse-grained, 
compact. Easily worked. 
Polishes. Durable in con- 
tact with the soil. Use : 
Building material and 
general use 



Spruce (Black) 

Color light red or often 
nearly white; sap-wood 
lighter. Wood light, soft, 
not strong, close, 
straight-grained, com- 
pact, satiny. Use : Piles, 
lumber. 



Spruce (White) 

Color light yellow ; sap- 
wood hardly distinguish- 
able. Wood light, soft, 
not strong, close, 
straight-grained, com- 
pact, satiny. Use : Lum- 
ber for construction. 

Walnut (White) {Butter 

nut) 

Color light brown, 
turning dark on expo- 
sure. Light, soft, coarse- 
grained, compact. Easily 
worked. Satiny. Polishes 
well. Use: Interior finish 

Walnut (Black) 

Color rich dark brown; 
sap-wood lighter. Heavy, 
hard, strong, coarse- 
grained. Checks if not 
carefully seasoned, 
Easily worked. Polishes. 
Use: Interior finish, cabi- 
net-work. 



30 



26.23 



28.57 



25.25 



25.46 



38.11 



Resistance to 



Ten- 
sion. 



Crush- 
ing. 



Cross- 
break- 
ing. 



Shearing. 



With 

the 

Grain. 



Across 

the 
Grain. 



Pounds per Square Inch. 





8 


g 








fe 


rj« 








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CO 


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Tf 


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62 TIMBER. 

Seasoning Timber. 

The seasoning of timber consists in expelling, as far as possible, 
the moisture which is contained in its pores. Two methods are 
practised, natural and artificial. 

Natural Seasoning is performed simply by exposing the tim- 
ber freely to the air in a dry place, piled under shelter. The 
bottom pieces should be placed upon skids (which should be free 
from decay), raised not less than two feet from the ground. It 
should be piled in horizontal layers with slats or piling- strips 
placed between each layer, one near the end of each pile and others 
at short distances, in order to keep the timber from winding: these 
strips should not be less than one inch thick. Each pile should 
contain but one description of timber and the piles should be placed 
at least 2^ feet apart, so as to allow free circulation of the air. 

The timber should be replied at frequent intervals, and all 
pieces indicating decay should be removed, to prevent their affect- 
ing those which are still sound. 

The time required for natural seasoning varies according to the 
character of the wood and its dimensions. 

The following table shows the average time required for the 
woods named : 

White-pine board 1 year 

'' plank 2 in. thick 1^ *' 

" 3 '' '' 2 ** 

Southern heart-pine 1 in. thick 1 * * 

Black walnut 1 '' '' 1^-2 " 

tt (t 4 *' '* 4 ** 

Hemlock will dry out sufficiently to be used as joists in from 
five to seven months ; oak and ash approximate walnut in the 
length of time required. 

Water Seasoning is total immersion of timber in water for 
the purpose of dissolving the sap, and when thus seasoned it is 
less liable to warp and crack, but is rendered more brittle, and if 
kept too long immersed will upon being brought into the air be- 
come brashy and useless. Two weeks is about the usual time it is 
kept under water. After removal from the water it must be thor- 
oughly dried, with free access of air, and turned daily. 

Artificial Seasoning. — The best method consists in exposing 
the timber to a current of hot air in a drying-kiln. The best 
temperature for the hot air varies with the kind and dimensions 



TIMBER. 63 

of the timber ; thus for oak the temperature required is about 
105" F. and for pine 180° to 200° F. 

The time required for drying varies with the thickness. 

Too high temperatures evaporate the moisture too rapidly, 
and the timber cracks. 

Shrinkage and Expansion of Timber. 

During the drying or seasoning process timber shrinks consider- 
ably ; below about 30 per cent of moisture it shrinks nearly as 
much as it dries ; that is to say, when timber dries down from 30 
per cent of moisture to 10 per cent moisture it dries out or loses 
in weight about 20 per cent of its dry weight. It also loses about 
20 per cent of its dry volume. A board that is 1 foot wide at 30 
per cent moisture is only llf inches wide at 10 per cent moisture. 
or a board 4 inches wide at 20 per cent moisture is only about 
3| inches wide at 10 per cent moisture The shrinkage lengthwise 
is very slight. 

On account of the very large radial fibres (medullary rays) in 
oak wood this kind of timber shrinks mostly in a circumferential 
direction, and all timber shrinks more circumferentially than 
radially, since all woods have those medullary rays to a greater or 
less extent. It is for this reason that ** quarter-sawed " (radial- 
sawed) lumber is more satisfactory than *' flat-sawed " for all kinds 
of furniture and house trimmings. For flooring, quarter-sawed 
or ** rift-sawed" boards, presenting an "edge-grain" surface, 
is far preferable to " flat-grain," because it wears evenly and does 
not sliver on the surface. 

The shrinkage of different woods is about as follows: 

Cedar Canada from 14 to 13.25 inches 

Elm ,... '* 11 '* 10.75 *' 

Oak " 12 '• 11.625 '' 

Pine (Northern pitch) *' 10x10 " 9.75X9.75 " 

*' (Southern pitch) *' 18.375'* 18.25 *' 

*• (white) *' 12 '' 11.875 " 

'* (yellow Northern) '* 18 *' 17.875 *' 

Spruce *' 8.5 '* 8.375 " 

Expansion of Timber due to the Absorption of Water. 

Pine. Oak. Chestnut. 

Elongation, per cent 0.065 0.085 0.165 

Lateral expansion, per cent ^.6 3.5 3.63 



64 " TIMBER. 

Expansion of Timber by Heat. 

White pine for 1 degree F. 1 part in 440.530 or for 180 degrees 
1 part in 2447, or about one third of the expansion of iron. 

Durability and Decay of Timber. 

The durability of wood is subject to too great variation to have 
any limits placed upon it, depending almost entirely upon the 
conditions to which it is exposed, as to heat and moisture, attacks 
of insects, etc. Well- seasoned wood in dry situations or in well- 
ventilated situations with uniform state of moisture or dryness 
(moisture preferred) should never decay. Timber kept constantly 
wet may become softened and weakened, but it does not necessarily 
decay. Various kinds of timber, such as elm, alder, oak, and 
beech, possess great durability in this condition. 

The condition which is least favorable to durability is alternate 
wetness and dryness, or a slight degree of moisture, especially if 
accompanied by heat and confined air. 

The season and manner of felling and working are important in 
determining the life. Timber felled in winter is more durable 
than that felled in summer. Hewed wood is also more durable 
than sawed from the fact that the pores are closed and the fibre 
compacted by the blows, while the saw tears the fibre and opens it. 
Besides decomposition and decay, timber both in its growing 
and converted states is subject to the attacks of worms and 
insects ; these are often selective in their attacks ; the resinous 
woods, iron wood, and palmetto are not readily attacked. When the 
insects exist in large numbers they remove so much of the wood 
as seriously to impair its strength. 

Dry Rot is the most formidable kind of decay to which timber 
is subject. It is caused by a fungus, whose spawn in the sap- 
wood, on the introduction of moisture, causes fermentation, and 
the decay of the tissues follows, and in a short time the wood will 
crumble beneath the touch. 

Dry rot occurs most frequently in ill-ventilated places. The ends 
of timbers built into walls, woodwork fixed to walls before they 
are dry, are quickly affected. Painting and tarring the surface of 
unseasoned timber has the same effect. An excess of moisture 
prevents the growth of the fungus, but a moderate warmth, com- 
bined with damp and want of air, accelerates it. 

The season of felling influences the resistance to dry rot, tim- 
ber felled in winter being less liable to attack, but the germs of 



TIMBEE. 65 

decay may remain inert in the wood for a long time, and finally 
become evident and active if tlie conditions be favorable. Once 
established in the wood it is very difficult to eradicate, the only 
remedy being to remove all trace of the fungus and disinfect. 

Healthy wood is liable to receive germs from the air and water, 
and these sources are of more danger than the germs contained in 
the wood itself. 

The colors of the fungus are various: sometimes white, grayish 
white with violet, often of yellowish brown or a deep shade of 
fine rich brown. 

The softer and more porous woods are the more liable to decay 
by dry rot. 

Detection of Dry Rot.— In the first stages of rottenness the 
timber swells and changes color, and is often covered with fungus 
or mouldiness, and emits a musty odor. 

In the absence of any outward fungus or other visible sign a 
hole may be bored into the wood : the appearance of the dust 
extracted and especially the odor will indicate the presence of dry 
rot. 

Sometimes the rot only appears in the form of reddish or yellow 
spots, which upon being scratched show that the fibres have been 
reduced to powder. 

Wet Rot is caused by the presence of moisture, which decom- 
poses the tissues of the wood, particularly those of the sap-wood. 
Wood felled between April and October is especially liable to wet 
rot. 

Common Rot is caused by the wood being piled to season in 
badly ventilated sheds. Outward indications are yellow spots upon 
the ends of the pieces, and a yellowish dust in the checks and 
cracks, particularly where the pieces rest upon the piling-strips. 

Worms.— Of worms the two most active are the Teredo navalis 
and the Limnoria terebrans. The Teredo is most active in salt 
water. It is found in both warm and cold climates. It avoids 
fresh water and prefers clear water to that which is muddy. 

The Teredo is first deposited upon the timber in the shape of an 
egg, from which in time it emerges a small worm ; this worm 
soon becomes larger and commences its depredations. 

Furnished with a shelly substance in its head, shaped like an 
auger, it bores into the wood, in an upward course parallel to the 
grain; at the same time it lines the hole it makes with a thin 
coating of carbonate of lime, and closes the opening with two 
iSmall lids ; hence it prefers a calcareous seashore. 



66 TIMBER. 

As tlie work of the Teredo advances its size increases. Worms 
two feet long and three fourths inch in diameter have been found. 

The Limnoria terebrans resembles in appearance a very small 
wood-louse and is most active in brackish water and prefers a 
silicious shore, formed by the decomposition of silicious rocks. 
As many as twenty thousand will appear on a surface only twelve 
inches square. The Limnoria prefers soft woods and avoids 
knots ; it does not bore, but destroys the wood by eating the surface 
at the rate of from one to three inches per annum. 

Both the Teredo and Limnoria confine their work to a space 
between high- and low- water marks, showing that they require 
both air and water. 

The Lycoris fucata is the enemy of the Teredo ; it is a little 
worm with legs, something like a centipede ; it lives in the mud, 
crawls up the pile inhabited by the Teredo, enters the tunnel in 
which it is ensconced, eats the Teredo, enlarges the entrance to 
the tunnel, and then lives in it. 

Many processes have been tried to protect timber from the 
ravages of those worms ; the most successful appears to be^ 
impegnation with creosote. 

Processes for Preserving Timber. 

From the earliest times attempts have been made to preservi 
wood, and a vast number of processes and materials have bee: 
experimented with. A few of the successful methods are as fol- 
lows: 

Burnett's Process, or Burnettizing. — Impregnation with 
chloride of zinc. The operation is performed in large metal 
cylinders called retorts, and is conducted about as follows: The 
load of timber, called a "charge," is placed in the retort and the- 
heads or doors closed and bolted. A vacuum is then produced iifl 
the retort. When this has reached about twenty inches live steam 
at about 20 pounds' pressure is let in and continued for about four 
or five hours. It is then blown off and the retorts drained 
second vacuum is produced of from twenty-two to twenty-si: 
inches. The zinc chloride solution is introduced under pressure 
this pressure is raised to about 120 to 150 pounds per square inch 
and maintained until the required quantity of solution is injected 
into the timber; when this has been accomplished the surplus 
fluid is drawn off, the doors opened, and the charge pulled out. 

The solution of zinc chloride, called the ''stock solution,*' con- 



ir 



TIMBER. 07 

sists of about 43 per cent pure zinc chlorine, 2 per cent of impu- 
rities (iron, aluminum, lead, etc.), and 55 per cent of water. The 
standard solution when ready for use should register 2^° Baume 
at 60° F. The solution is heated by steam passed through coils to 
about 150° F. before being pumped into the charge. 

To provide means for watching the effect of the various steps in 
the process the retorts are provided with thermometers and 
vacuum-gauges, the steam-pipes with pyrometers, the tanks with 
gauges, the condenser with a measuring- well, and the solution is 
taken from a gauged measuring- tank. 

The quantity of zinc injected per cubic foot of timber is about 
Y%% of a pound. The time required for treatment ranges from 8 
to 12 hours, depending upon the condition of the timber ; the 
greener the wood the more easily it is impregnated. 

Burnettizing has not been so successful in the United States as 
in Europe. 

Wellshouse's Process is a modification of Burnett's. The 
timber is steamed in a cylinder one to three hours (according to 
size); zinc chloride and glue solution is then forced in, after which 
tannin is injected, the purpose of the glue being to combine with 
the tannic acid in the wood, precipitating the glue as an insoluble 
compound and retaining the zinc. The tannic acid is added to 
precipitate the excess of glue. 

Thilmany's Process. — Impregnation with zinc or copper sul- 
phate. For this process green wood is preferred, the dry requiring 
to be longer steamed. The timber is run on flat cars into a cylinder, 
steam is applied to drive out the sap, and an air-pump is connected 
to draw air and condensed moisture and form a vacuum. The 
cylinder is then filled with a 1^ per cent solution of zinc or copper 
sulphate and a pressure of 80 to 100 pounds applied until chaiged. 
The sulphate solution is then drawn off and a 1 per cent solution 
of barium chloride similarly charged. The strength of the solu- 
tion is varied according to the class of timber to be impregnated. 
Kyan^s Process. — Saturating with corrosive sublimate. 
Boucherie's Process. — Impregnation with sulphate of copper 
under a pressure of about 15 lbs. per sq. in. 

Creosoting (Betiiell's Process). — Impregnating with dead 
oil of coal-tar or distillates from wood-tars. 

The timber is placed in cylinders, steam turned on and continued 
until the mass is thoroughly heated and the sap va orized. The 
steam and sap are drawn off by a pump, a partial vac-uuin formed, 
and the cylinder filled with the oil, which is usually heated to a 



68 TIMBER. 

temperature of about 160°. A pressure varying from 150 to 200 
lbs. is applied and continued until the gauge stands constant, 
showing that no more oil is being absorbed. The oil is then 
drawn off and the charge removed. 

The details of the operation vary in different establishments. 
The time required for steaming varies from 30 minutes to several 
hours according to the variety of wood under treatment, green and 
hard timber requiring more than seasoned or soft timber. The 
amount of oil absorbed by the timber also varies according to its 
variety ; from 12 to 18 pounds per cubic foot appears to be the 
usual amount. The treatment of a charge requires on an average 
24 hours. 

Payne's Process. — Impregnating the wood while in a vacuum 
with sulphate of iron, followed by a solution of sulphate of 
lime or soda. This process is also said to render the wood incom- 
bustible. 

Seeley's Process is a modification of Bethell's. The timber is 
immersed in creosote at a temperature of 212° to 300° F. for a 
time sufla.cient to expel the moisture, the hot oil is drawn off and 
replaced by cold oil. About 4 lbs. per cubic foot is said to be 
absorbed by this process. 

Vulcanizing is the process of rendering the sap insoluble and 
undecompcsable within the cells by means of heat. To do this 
the wood is subjected to such pressure of air, in a closed vessel, 
that the sap will not vaporize on the application of heat. Heat is 
then applied gradually, the pressure being maintained or increased 
as the temperature rises. About 400° F. is generally sufficient to 
vulcanize ordinary woods. The time required is about 8 hours for 
soft and from 10 to 20 hours for hard woods. 



TIMBER. 69 



Inspection of Treated Timber. 

Inspect for penetration by boring two |-inch holes at a distance 
of from 3 to 15 feet from each end, according to the length of 
the stick ; the two holes near each end to be diametrically oppo- 
site, and the pair on one end to be at right angles to that on the 
other. In special cases other holes may be bored. Care must be 
taken not to bore into a check. After inspection the holes are to 
be plugged with preserved plugs turned to a driving fit. 

Testing Timber treated with Zinc Chloride. — At inter- 
vals during the progress of the impregnation and whenever any 
charge shows some change in the treatment as to vacuum, lime 
or amount of pressure, and after each change in kind, quality, or 
dryness of timber four samples are taken from a charge consist- 
ing of pieces of average grain — one heaviest, one lightest, and two 
average weight. Each piece is bored in the middle of its width 
and length with a one-inch auger. The first half inch of the 
borings is thrown away, after which each inch of borings is pre- 
served separately and designated as 1-inch, 2-inch, 3-inch, etc., 
specimens. Each specimen is burned to an ash, over a gasoline 
jet, in a porcelain roasliug-dish, in contact with the air. The 
ashes are carefully collected in a platinum cup, distilled water 
added, with a slight excess of hydrochloric acid, converting the 
zinc oxide into zinc chloride. It is then filtered into a test-tube 
and the zinc hydrate thrown down with sodium carbonate, mak- 
ing a white flocculent precipitate. The liquid is then made up 
with distilled water to three drachms. The resulting milky liquid 
is compared with standard liquids in tubes of the same size as the 
test-tubes, each tube containing three drachms. The standard 
liquids are graded to represent 6, 9, 12, 15, 18, 21, and 24 one- 
hundredths of a pound of zinc chloride per cubic foot of timber. 
The maximum of zinc chloride per cubic foot of timber is 24 
oue-hundredths of a pound. 



70 TIMBER. 

Form op Report. 

WOOD-PRESERVING. 

Beport of Creosotedat. 



189. 

Retort No 

Kind of timber 

Charge number. . . . 

Date going in 

Date coming out 

Time : Load in at 

Pressure began at 

Pressure left off at 

Load out at 

Total time 

Temperature : When filled 

At end of pressure when oil is let out of 

steam 

Pressure : At beginning 

At end 

Condensation ; Quantity of oil pumped 

Number of pieces in charge 

Number of cubic feet in charge 

Length, bread tii, and thickness of pieces. . . 

Maximum penetration: Ends Centre. 

Minimum penetration: Ends Centre. 

Amount of creosote per cubic foot 



Form of Report. 

wood-preserving. 
Report of, Burnettized at. 



189, 

Retort No 



Charge number. . , . 

Date going in 

Date going out 

Number of pieces in charge. . . . 
Length, breadth, thickness. . . . 
Number of cubic feet in charge. 



TIMBER. 71 

Time ; Charge in at 

Vacuum begun at 

Inches of vacuum. . . . 

Steam turned in at 

Steam-pressure 

Vacuum begun at » o 

Injection begun at 

Pressure begun at 

Pressure left off at 

Charge out at 

Total time 

Temperature: At end of live steam 

When injection began. ... 
At end of pressure. ... 
When solution is let off . . . . 

Pressure : At beginning 

At end 

Quantity of solution pumped in . . . 

Quantity drawn off 

Report of Tests. 

Piles : Number of specimens tested. ... 

Length of piles • 

Diameter of piles 

Maximum penetration : Butt Tip 

Minimum penetration : Butt Tip 

Timber : Number of pieces tested. . . . 

Length 

Breadth 

Thickness 

Weight 

Solution, and penetration per cubic foot 

Remarks: Penetration uniform or irregular 

Depth of penetration 

Effect on timber — splitting, checking, or cracking. .. 



n 



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I 



TIMBER. 73 



Measurement of Timber. 

Timber is measured when bought iu the market either by the 
cubic foot or by hoard measure. The unit of the latter is a square 
foot of surface by one inch in thickness, and is denoted by the 
abbreviation B. M. 

Rule. — Multiply together the three dimensions, width and 
thickness in inches and the length in feet, divide the product by 
12, and the quotient will be the board measure. 

Sawn or hewn timber is often measured by the cubic foot. 

Round timber is measured by multiplying the length by the 
square of one-fourth its mean girth to obtain the cubic contents. 

When the length is given i?ifeet, and the girth in inches, multi- 
ply as above and divide by 144. 

When all the dimensions are in inches^ multiply as above and 
divide by 1728. 

1000 feet board measure = 83i cubic feet. 



Inspection of Timber, 

In examining timber the points to be observed are quality 
and dimensions. All condemned pieces should be marked with 
paint or a branding-iron. 

Appearance of Good Timber. — There are certain appear- 
ances which are characteristic of strong and durable timber, to 
what class soever it belongs. 

In the same species of timber that specimen will in general be 
the strongest and the most durable which has grown the slowest, 
as shown by the narrowness of the annual rings. 

Good timber should be from the heart of a sound tree, the sap 
being entirely removed, the wood uniform in substance, straight 
in fibre, free from large or dead knots, flaws, shakes, or blemishes 
of any kind. 

If freshly cut it should smell sweet. The surface should not 
be woolly, or clog the teeth of the saw, but should be firm and 
bright, with a silky lustre when planed. A disagreeable odor 
indicates decay, and a dull, chalky appearance is a sign of bad 
timber 

Good timber is sonorous when struck. A dull, heavy sound 
indicates decay. 

Amongst resiuous wood^ those which have least resin in their 



74 TIMBER. 

pores, and amongst non-resinous woods those wliicb have least sap 
vor gum in them, are in general the strongest and most lasting. 

Among colored woods, darkness of color is in general a sign of 
»lrengih and durability. 

If a piece of sound timber be struck lightly with a small ham- 
mer or scratclied at one end, the sound can be distinctly heard by 
a person placing his ear against the other end, even if the stick 
be 50 ft. long; but if the timber be decayed, the sound will be 
very faint. 

Defects of Timber, 

Wind shakes. — Circular cracks separating the concentric 
layers of wood from each other. Tliey are serious defects. 

Splits, Checks, and Cracks, extending toward the centre, 
if deep and strongly marked, render timber unfit for use, unless 
the purpose for which il is intended will admit of its being split 
through them. 

Brashy Timber. — Timber from troes which have commenced 
to decay from old age ; indicated by a reddish color, breaking of 
the wood without splinters, and porosit3^ 

Belted is the term applied to timber which has been killed 
before being felled. Such timber is objectionable. 

Knotty is the term applied to timber containing many knots. 
The knots, though sound are objectionable when they extend far 
inwards. 

Twisted is the term applied to timber in which the grain 
winds spirally; such timber is unfit for long pieces. 

Heart-shake. — Splits or clefts in the centre of the tree. 

Star-shakes. — Several splits radiating from the centre. 

Cup-shakes. — Curved splits separating the rings wholly or in 
part. 

Rind-gall. — Curved swelling, usually caused by growth of 
layers over a spot where a branch has been removed. 

Upset. — Fibres injured by crushing. 

FoxiNESS. — Yellow or red tinge, indicating incipient decay. 

Dote — Doatiness. — A disease indicated by speckled stains 
and dulness of sound when struck a quick blow. 



TIMBER. 



75 



To Determine Amount of Moisture in Lumber. 

To determine the amouDt of moisture in lumber, cut a section 
from a board or stick and weigh it; then dry it in an ordinary 
stove-oven with a slow fire for an hour or two; then weigh again. 
The difference in weight divided by the dry weight is the per- 
centage of moisture. 

** Thoroughly dry lumber " should not contain more than 10 
or 13 per cent of water, and the interior should be as dry as the 
exterior. 

The amount of water contained in wood varies within very 
wide limits. 



Willow 26.0 per cent 



Mountain ash. . 

Oak 

Horse-chestnut 

Elm 

Poplar (white). 



28.3 
34.7 
38.7 
44.5 
50.2 



Sycamore 27.0 per cent 

Beech 30.8 ** '' 

Fir (white) 37.1 ** *' 

Alder 41.6 *V '* 

Fir (red) 45.2 *' ** 

Poplar (black) . . 51.8 ** " 



By ** air-drying" the water is not entirely removed; the evapo- 
ration continues until an equilibrium is established between the 
humidity of the air and the hygroscopic power of the wood. 
By heat, however, 16 to 20 per cent more can be expelled, but at 
such temperatures that the wood is liable to become brown and 
decompose. By air-drying 20 to 25 per cent of water can be 
expelled by from 10 to 12 months' exposure. 



absorptive power of wood. 



Kind of Wood. 



Black gum 

Cottonwood 

Oak 

Spruce 

'' (burnettized, .2500) 

Hard pine 

White birch 

Sesquoia gigantea of California, 



Percentage of Water Absorbed. 



Dry Wood. 



1.0000 

.7140 

.2000 

.1754 to .3333 

.1600 
.4300 
.4722 



Creosoted. 



.1250 

.3470 

.0625 

.0236 to .0306 

.0000 
.1240 
.0000 



76 TIMBER. 



General Rules for Classifying Lumber.* 

Tbe following general rules are intended to serve as a guide in 
classifying lumber in accordance with tbe grades named below. 
While they are intended to apply only to Southern yellow pine, 
tliey can be understood to apply in a general way to all mer- 
chantable lumber. 

Yellow-pine Lumber shall be graded and classified accord- 
ing to the following rules and specifications as to quality; and 
dressed stock shall conform to the subjoined table of standard 
sizes, except where otherwise expressly stipulated between buyer 
and seller. 

Recognized Defects in Yellow Pine are knots (pin, round, 
spike, black, encased, loose, or rotten), knot-holes, splits (either 
from seasoning, ring-heart, or rough handling), rotten streaks y 
dote, rot, worm-holes, and pitch-pockets. 

Shake. — *' King-heart " is a shake or cleavage along the plane 
of an annual ring, usually about half-way between the pith and 
the circumference. *' Shake,'' or " wind-shake," is a cleavage of 
the trunk of a tree, while yet standing, due to the action of the 
wind in bending the trunk. It is usually along the plane of an 
annual ring, that is to say, concentric with the centre or pith of 
the tree. '* Heart-shake" is a diametrical or radial cleavage 
through the tree or log. If it occurs after the logs are cut, or in 
large timbers after they are sawed, it is due to shrinkage in dry- 
ing. Tliis is a common defect of all oak logs or large timbers. 

Wane is a deficiency in width, either over the entire edge or 
on one corner, caused by a crook in the log. 

Crooks are permanent distortions of the board, due to defec- 
tive piling or from other causes. 

Waup is a twisting of the board into a warped surface. 

Seasoning- or Kiln-checks are either very small or large 
cracks caused by drying the surface of the board, with its 
accompanying shrinkage, while the interior is still wet. 

Blue Sap, a discoloration which green yellow pine is subject 
to, especially the sap portion, if not at once piled for drying or 
placed in a dry kiln. 

Pitch-streaks are longitudinal openings, sometimes of con- 
siderable size, as J to :|^ inch wide and several inches, or even 
feet, long, filled with resin. 

♦ Adopted by tbe Southein Lumber Manufacturers' Association, 1895, 



TIMBER. ^ 77 

Bright Sap shall not be considered a defect in any of the 
grades provided for and described in these rules. The restric- 
tion or exclusion of bright sap constitutes a special class of 
material, which can be secured only by special contract. 

Firm Redheart shall not be considered a defect in common 
grades. 

Defects in Rough Stock, caused by improper manufacture 
or drying, will reduce grade, unless they can be removed in 
working such stock to standard sizes. 

Imperfect Manufacture in dressed stock, such as cMpped, 
grain-splintered or torn places, broken knots on edge of ship-lap, 
insufficient tongue on flooring, etc., shall be considered defects, 
and reduce grade accordingly. 

A Standard Knot is sound, and not over 1^ inches in diameter. 

A Pin-knot is sound, and not over ^ inch in diameter. 

Any piece that will not work one half its size shall be classed 
as a dead cull. 

The Grade of all regular stock shall be determined by the 
number and position of the defects visible in any piece. The 
enumerated defects admissible in any given grade are intended 
to be descriptive of the coarsest pieces such grade may contain. 
The average quality of the grade should be midway between 
such pieces and the defects allowed in the next higher grade. 

Lumber or timber sawed for specific purposes, as bridge timbers, 
etc., must be inspected with a view to the adaptability of the 
piece for the use intended. 

In finishing, flooring, etc., the enumerated defects admissible 
in a given grade apply only to the face side of the piece, but the 
reverse face should not admit defects that would render the piece 
unsuitable for the purpose intended. 

Standard Lengths are multiples of 2 feet from 10 to 20 feet, 
inclusive, for boards and strips, and from 10 to 24 feet, inclusive, 
for dimension joists and timbers. Longer or shorter lengths 
than those herein specified are special. Odd lengths, if below 24 
feet, shall be counted as of the next higher even length. 

On stock shipments of 8-inch and under no board shall be 
admissible that is more than I inch scant; on 10-inch not more 
than I inch, and on 12-inch not more than ^ inch scant of speci- 
fi'd width. 

Yellow pine of better grade than No. 1 common up to 4 inches 
in width is classified according to grain, ^s edge-grain and flat- 
grain. Edge-grain yellow pine has been variously designated as 



■^78 TIMBER. 

"rift sawn," ''straight-grain," *' vertical -grain/' and " quarter- 
si wed," all being commercially sj^nonymous terms. Edge-grain 
stock is specially desirable for flooring, and admits no piece in 
which tlte angle of the grain exceeds 45 degrees from the vertical 
thus excluding all pieces that will sliver or shell from weai 
Such stock as will not meet these requirements is known as fla1 
grain. 

All dressed and matched stock shall be measured and sold 
"strip count," 1. e., full size of rough strip from which such 
stock is made — 3, 4, 5, and 6 inches. 

The foregoing general observations shall apply to and govern 
the following detailed descriptive enumeration of recognize* 
grades. 



in 

I 



Rules for Grading Finished Lumber. 



1 



The following rules for grading apply to all kinds of finishing 
stock, whether for interior or outdoor work. In these rules the 
expressions ** S. IS." or " S. 2S." mean "surfaced one side" or 
"surfaced two sides," respectively Also "S. IS. IE." mean 
"surfaced one side and one edge." By surfacing is meant 
planing or running it through a planing-machine. It may still 
require hand-dressing for the best work. Nearly all sawmills 
now dry their lumber and run it through the planer in order to 
save the extra freight on the lough and green lumber. 

Grades. — First and second clear; third clear, barn and roofing 
stocks. 

First and Second Clear Finish. — 1 inch, IS. or 2S., up to 
and including 10 inches wide, must show one face clear from all 
defects; 33^ per cent of any shipment of boards 12 or 14 inches 
wide will admit two pin-knots or one standard knot, slight pitch- 
streak, or small pitch-pocket, or sap stain not over H inches wide 
running across the face, or small kiln- or seasoning-checks, but 
no two of these defects shall appear in a single piece; 16-inch 
wide will admit of two defects allowed in 12-inch or their equiva- 
lent; wider than 16-inch will admit proportionately more defects. 
Pieces otherwise admissible in which the point of the grain has 
been loosened or slivered in dressing one face side should be put 
in lower grade. Defective dressing on reverse face of finishing is 
admissible. In case both faces are desired clear special contract 
must be made. 

Third Clear Finish. — 1 inch, S. IS. or 2S., up to and in- 
cluding 10 inches wide, may have not more than two of the 



TIMBER. V9 

following defects on best or face side: three pin-knots, one 
standard knot, three sap-stains 2 inches wide running across the 
face or their equivalent, two pitch-pockets, slight pitch streaks 
kiln or seasoning checks, torn places, and wane which does not 
enter more than 1 inch, nor extend more than 2 feet; 12-inch 
will admit three of the above defects or their equivalent. This 
grade is suitable for paint finish. 

IJ, 1|, and 2 inch, S. 1 or 2 S., shall take 1-inch inspection, and 
unless otherwise agreed between buyer and seller, shall be sub- 
ject to inspection on face or best side onl3^ 

Barn and Novelty -siding, Ship-lap and Grooved Roofing 
shall be 8, 10, and 12 inches wide, and consist of boards below 
third clear which are sound and water-tight, free from coarse 
knots, and wane over 1 inch wide and extending more than 3 feet 
in any piece. Pitch, except in narrow streaks, should be excluded. 

Edge-grain Flooring. (Grades : First Clear, Second Clear). 
— First clear edge-grain flooring must be well manufactured, and 
free from all defects on face side of strip. 

Second clear edge-grain flooring will admit of three pin-knots, 
or one standard knot, or small pitch-pocket, or blue-sap stain not 
to exceed 10 per cent of the face. 

Flat-grain Flooring. (Grades : A flat, B flat.) — A-flat floor- 
ing may contain two pin-knots or one small pitch-pocket, but 
shall be free from other defects, and must be well manufactured. 
Pieces in which the point of the grain has been loosened in dress- 
ing should be put in lower grade. 

B-flat flooring may have any tw^o of the following defects : 
Three pin-knots or one standard knot ; slight sap-stains, slight 
torn places and defects in manufacture, narrow pitch-streaks, and 
seasoning-checks. When all other defects are absent, blue-sap 
stain in any quantity shall be admitted. 

Common Flooring. (Grades : No. 1 Common, No. 2 Common.) 
— No. 1 Common must be manufactured from sound stock. In 
addition to the defects described in B flat, also admits of sound 
knots, blue sap and firm redheart in any quantity, pitch, and 
slight shake, but must "lay" without waste. No division as to 
grain is made in this grade. 

No. 2 Common Flooring includes all pieces that will not 
grade No. 1 common, which can be laid without wasting more 
than one-fourth the length of any piece. This grade will admit 
imperfections which do not render the piece unfit for use in cheap 
floors and roof-sheathing. 



80 TIMBER. 

Centre-matched Flooring shall be required to come up to 
grade on cue face only. 

Ceiling. (Grades : A, B, C.)—A ceiling shall be free from all 
defects on face, and well manufactured. 

B Ceiling will admit slight imperfections in dressing. Three 
pin-knots, or oue standard knot, pitch-streaks or small pitch- 
pockets, or blue sap-stain not lo exceed 10 per cent of the face ; 
but not more than two of these defects to be admitted in any 
piece. 

C Ceiling conforms to grade No. 1 common flooring, and is 
suitable for paint finish. Will admit imperfections that do not 
prevent its use without waste. 

Wagon Bottoms. (Grades : A, B.) — Wagon bottoms shall be 
graded the same as flat-grain flooring. 

Bevel and Dkop Siding. (Grades: A, B, C.) — Shall be graded 
according to ceiling rules, but will admit more blue stain, and, 
except in grade C, should exclude pitch. Slight additional im- 
perfections on the tliin edge of bevel-siding which will be covered 
by the lap are admissible. 

Partition. (Grades : A, B, C.)— Partition shall conform to 
ceiling grades, but must meet the requirements of the specified 
grade only on one face. The reverse face shall not be more than 
one grade lower. 

Moulded Casings and Base. (Grades • First Clear, Second 
Clear.) — First clear shall be free from all defects on face and 
perfect in manufacture. 

Second clear is suitable for work that is to receive a paint finish, 
and usually consists of rejections, made after dressing, from stock 
inspected in the rough as first clear. The defects admitted in B 
ceiling would be allowed. 



TIMBEB. 81 

Rules for Grading* Common Boards and Rough 
Lumber. 

Common Boards and Ship-lap. — No. 1 common boards, S. 
IS., and Ko. 1 common ship-lap shall be manufactured from 
sound slock, of even thickness the entire length. Will admit 
of any two of the folio wing defects: Wane one-half inch deep on 
edge and one sixth the length of the piece; tight sound kuots, 
none of which shall be larger than three inches in diameter, or 
equivalent spike-knots ; one split not more than 16 inches long; 
and blue sap. These boards shall be firm and strong, suitable for 
use in all ordinary construction, and serviceable without waste. 

No. 2 Common Boards and No. 2 Common Ship-lap admit 
pieces that fall below No. 1, which are free from the followiog 
defects: Rotten streaks that go through the piece, through heart- 
shakes which extend more than half the length of the piece, and 
wane over 2 inches wide, exceeding one third the leugth of the 
piece. A knot-hole IJ inches in diameter or its equivalent will 
be allowed, provided the piece would otherwise grade No. 1 com- 
mon. Worm-holes and straight splits one fourth of the length of 
the piece are admissible. 

Fencing, S. IS. — No. 1 Common Fencing must be manufac- 
tured from* sound stock. May contain sound knots equal in di- 
ameter to not over one third the width of the piece at any given 
point throughout its length, but must be free from spike-knots 
the length of which is over half the width of the piece. Also, 
free from wane over \ inch deep on edge and one half the length 
of any piece measured on one side. This grade must work its 
full length without waste. 

No. 2 Common Fencing shall admit of pieces that fall below 
No. 1 common which are free from through rotten streaks. 

Miscut 1-inch stock in boards and fencing which does not fall 
below f inch thick shall be admitted in No. 2 common provided 
that the grade of such thin stock is in all other respects as good 
as No. 1 common. 

Dimension S. IS. IE. — No, 1 Common Dimension shall be 
manufactured from sound stock, and be free from loose and un- 
sound knots, and large knots so located as to materially impair 
the strength of the piece; will admit of seasoning-checks and 
heart-shakes that do not go through, of slight wane and such 
other defects as do not prevent its use as substantial structural 
m tsrial 



82 TIMBER. 

No. 2 Common Dimension admits all pieces falling below No. 
1 common which aie free from through rotten streaks and sound 
enough to be used without waste. 

Miscut 2-inch stock which does not fall below 1^ inches shall 
be admitted in No. 2 common provided that the grade of such 
thin stock is in all other respects as good as No. 1 common. 

In boards, fencing and dimension stock falling beloyv No. 2 
grade and excluding dead culls shall be classed as No. 3. 

Dressed Timbers shall conform in grade to the specifications 
applying to rough limbers of similar size. 

Rough Yellow Pine. Flooring- strips and Finishing. — 
Flooring-strips are 3, 4, 5, and 6 inches wide when green; square- 
edged and evenly manufactured. 

Finish must be evenly manufactured, and shall embrace all sizes 
from 1 inch to 2 inches thick by 6 inches and over in width. 

No finishing-lumber, unless otherwise ordered, should measure 
when dry and rough less than yL inch scant in thickness. No 
piece in any shipment of boards and strips shall be more than J 
inch scant on 6- and 8-iuch stock, | inch scant on 10- and ^ inch 
scant on 12-inch and wider stock. 

Wane and seasoning checks that will dress out in working to 
standard thicknesses and widths are admissible. 

Subject to the foregoing provisions rough finishing shall be 
graded according to the specifications applying to dress finishing. 
When like grade of both faces is required special contract should 
be made. 

Common Boards. Fencing and Dimension. — Rough com- 
mon boards and fencing must be evenly manufactured, and 
should not be less than i inch thick when dry, nor more than i 
inch scant of specified width. 

Rough 2-iNcn Common shall be evenly manufactured and not 
less than 1| inches thick when green, or If inches thick when 
dry. The several widths must not be less than i inch over the 
standard dressing width for such stock. The defects admissible in 
rougli slock shall be the same as those applying to dressed stock 
of like kind and grade, but such further defects as would disap- 
pear in dressing to standard size of such material shall be 
allowed. 

Rough Timbers 6x6 inches and larger shall not be more 
than \ inch scant when green, and be evenly manufactured from 
sound stock with not less than three square edges, and must 1 e 
free from knots that will materially weaken the piece. 



TIMBER. 83 

Timbers 10 X 10 inches may bave a 2 inch wane on one corner, 
or its equivalent on two or more corners, one fourth the lengUi of 
the piece. Other sizes may have proportionate defects. 

Seasoning- checks and shakes extending not over one eighth 
the length of the piece are admissible. 

Standard Dimensions of the Southern Ijiiniher 
Manufacturers' Association.* 

Flooring.—- The standard of 1" X 4" and 6'' shall be f|" X 
3i" and 5^-"; If inch flooring I3V'. 

Ceiling.— |-inch ceiling y^-inch; ^-inch /^-inch; f-inch ^^- 
inch; f-inch ^f inch. Same width as flooring. 

Finishing.— 1-inch S. IS. or S. 2S.to |f inch; If inch S. IS. or 
S. 2S. to lA-inch; 1^-inch S. IS. or S. 2S. to l^f inch; 2-inch S. 
IS. or S. 2S. to l|-inch. 

Boards and Fencing.— 1-inch S. IS. or S. 2S. to |f-inch. 

Dimension.— 2 X 



-2 X 4 inch S. IS 


IE. to If X 3f inches. 


2X6 


( a 


- - If X 51 " 


2X8 


( ti 


- - If X n - 


2 X 10 


< it 


- " If X 9| '' 


2 X 12 


t i < 


'' '' If X Hi '' 


4X 4 


' 1 inch off side and edge. 


4X 4 


' S. 4S. 


J inch off each side. 



Inspection of Yellow-pine Liumher. 

{Rules adopted hy the New York Lumber- Trade Association.) 

Scantling shall embrace all sizes from two to five inches in 
thickness and two to six inches in width. For example: 2x2, 
2X3, 2X4, 2X5, 2x6, 3 X 3, 3 X 4, 3 X 5, 3 X 6, 4x4, 
4x 5, 4 X 6, 5 X 5, and 5 X 6. 

Plank shall embrace all sizes from one and one-half to five 
inches in thickness by seven inches and up in width (IJ, 2, 2^, 3, 
3|, 4, 4^, 5 X 7 and up wide). 

Dimension Sizes shall embrace all sizes six inches and up in 
thickness by seven inches and up in width, including six by six. 
For example: 6 X 6, 6 X 7, 7 X '7, 7 X 8, 8 X 8, 8 X 9, and up. 

Stepping shall embrace one to two and one-half inches in 
thickness by seven inches and up in width. For example : 1, \\, 
IJ, 2, 2^ X 7 and up wide. 

* These particular dimensions cannot be assumed to hold for all parts of 
the country. 



84 TIMBER. 

RouGH-EDGK or Flitch shall embrace all sizes one inch and up 
in thickness by eight inches and up in width, sawed on two sidea 
only. For example: 1, IJ, 2, 3, 4 and up thick, by 8 and up 
wide, sawed on two sides only. 

Square-edged Inspection. 

Scantling shall be free from injurious shakes, unsound knots, 
or knots to impair strength; sap, no objection. 

Plank shall be free from unsound knots, wane through or 
round shakes; sap, no objection. 

Dimension Sizes. — Sap, no objection; no wane edges, no 
shakes to show on outside of stick. All stock to be well and 
truly manufactured, full to sizes, and saw-butted. 

Merchantable Inspection. 

Scantling shall show three corners heart free from injurious 
shakes or unsound knots. 

Plank, nine inches and under wide shall show one heart face 
and two-thirds heart on opposite side, over nine inches wide shall 
show two-thirds heart on both sides, all free from round or 
through shakes, large or unsound knots. 

Dimension Sizes. — All square lumber shall show two-thirds 
heart on two sides, and not less than one-half heart on two other 
sides. Other sizes shall show two-thirds heart on faces and show 
heart two thirds of the length on edges, excepting where the 
width exceeds the thickness by three inches or over; then it shall 
Bhow heart on the edges for one half its length. 

Stepping shall sliow three corners heart, free from shakes and 
all knots exceeding half an inch in diameter and not more than 
six in a board. 

Rough-edge or Flitch shall be sawed from good heart tim- 
ber, and shall be measured in the middle on the narrow face, 
free from injurious shakes or unsound knots. All stock to be 
well and truly manufactured, full to size, and saw-butted. 

Prime Inspection. 

Hcantling shall show three corners heart, and not to exceed 
one inch of sap on fourth corner, measured diagonally, free from 
heart, shakes, large or unsound knots. 

Plank shall show one entire heart face, on opposite face not 
exceeding one sixth its width of sap on each corDer, free from 



TIMBER. 85 

unsound knots. Through or round shakes; &ap to be measured 
on face. 

Dimension Sizes. — Ou all square sizes the sap on each corner 
shall not exceed one sixth the width of the face. When the 
width does not exceed the thickness by three inches, to show half 
heart on narrow faces the entire length; sap on wide faces to be 
measured as on square sizes. 

Rough-edge or Flitch shall be measured in the middle or 
narrow face inside of sap, free from shakes or unsound knots. 

Clear Inspection. 

Scantling and Plank shall be free of sap, large knots, or 
other defects. 

Dimension Sizes shall be free from sap, large or unsound 
knots, shakes through or round. 

Designations of the Trade. 

Resawed Lumber. — Lumber sawn on four sides. ! 

Rough-edge or Flitch. — Lumber sawn on two sides. i 

Timber.— Hewn only. j< i 

Merchantable Flooring. ^ 

1 in. and 1^^ in. in thickness and from 4 to 6 in. in width, 
shall show one face free from sap, and two-thirds heart the entire 
length on the opposite face. Shall be free from rot, split, shakes, 
and unsound knots. Sound knots to be allowed as follows, viz.: 
Two knots in boards under 10 ft. long; three knots in boards 16 
ft. long and over, of not over 1 in. in diameter, or six knots of 
not over J in. in diameter. 

Merchantable Flooring-plank. 

1| to 3 in. in thickness and 5 to 10 in. in width shall show one 
face free from sap, except on each edge of the face; i in. of sap 
shall be allowed and two-thirds heart on opposite face. Free 
from rot, split, shakes, unsound knots, and knots exceeding IJ 
in. in diameter. 

Merchantable Wide Boards and Plank. 

1 to 2 in. in thickness and 10 to 14 in. in width shall show one 
face free from sap, and two-thirds heart entire length on opposite 



86 TIMBER. 

face. Free from rot, through shakes, splits, and unsound knots; 
six sound knots of 1 in. and under in diameter, or three of IJ in. 
in diameter, to be allowed in any place. 

Prime Wide Boahds and Plank. 

1 to 2 iM. In thickness and 10 to 14 in. in width shall show one 
face and one edge free from sap, and two-thirds heart on the 
other face ; free from rot, shakes, splits, and knots. 

Merchantable Sidings. 

1 in., IJ in., and 1^ in. in thickness and 4 in. and over in width. 
Sap shall be allowed on the face, or best side (regardless of sap on 
the opposite face), as follows: ^ in. on one edge on boards 7 in. 
and under in width, and J in. on each edge of boards over 7 in. 
wide. Must be free from through shakes, rots, splits, and 
unsound knots; and on the face side the following allowance for 
knots shall be made, viz.: Three sound knots not exceeding 1 in. 
in diameter in boards under 14 ft. long; four sound knots not 
exceediug 1 in. in diameter in boards 14 ft. long and over, or six 
sound knots not exceeding ^ in. in diameter in boards of any 
length. In the measurement of boards, flooring, and sidings 1^ 
in. and under in thickness the fractions of a foot in contents less 
than nine twelfths shall be thrown off; six twelfths and over shall 
be counted as a foot. In the measurement of merchantable 
sidings, as to widths, they shall be measured whole and half inch 
only. For example: 4 in., 4^ in., 5 in., 5| in., 6 in., 6^ in., etc., 
wide. 

Kiln-dried Sidings and Flooring are inspected in the 
New York market as follows: Kiln-dried Saps, 1 in. and 1^ in. 
in thickness, 3 in. and up wide, 12 to 18 ft. long, small percent- 
age 10 and 11 ft., 90 per cent shall be free from knots and stain 
on one face, 10 per cent may have stain defects or a few sound 
knots. 

KouoH or Dressed Flooring, clear heart face rift or flat 
grain, to be free of knots, sap, or pitch-streaks on face side; No. 
1 flooring to be free of knots on face, but admitting bright sap. 



TIMBER. 87 

Inspection of White Pine, Spruce, etc. 

White Pine. — White pine plank and boards will frequently 
deteriorate in quality during the process of seasoning, or, more 
correctly speaking, imperfections which are entirely hidden 
when the wood is green become visible after it has dried out. 

White pine is graded into three qualities, viz., panel, common, 
and cullings. All boards and plank that shall not have more 
than three small sound knots, not more than half an inch in 
diameter, without sap or shake or any other defect or being free 
from knots and not having on an average more run of sap than 
half the thickness of the board or plank shall be deemed and 
counted sls panel. All boards and plank that shall not contain 
more than three — round— knots, not more than one inch in diam- 
eter, and not more run of sap than half the thickness of the board 
or plank, shall be deemed and counted as common. A split in the 
end of a board or plank nearly straight and not over two feet in 
length shall not condemn it to an inferior grade ; the split shall 
not vary more than half an inch to a foot from a straight line. 
All boards or plank that are rotten, worm-eaten, wind-shaken, 
or otherwise defective are classed as cullings. 

Spruce requires careful examination. The adhesion of the 
annual rings is very slight, and boards taken from the outside of 
the tree are liable to curl up and splinter when dried ; boards 
cut from sapliugs are subject to excessive shrinkage. Reject all 
waney pieces and those with knots and sap. 

White Pine Grades. — Each market assorts the grades to suit 
the local conditions. The following are the BuJBfalo, N. Y., 
grades : 

Terms Used. Thickness. Widths. Lengths. 

Uppers 1, IJ4, 1^, 2, 2i^, 3& 4 in.... 8 in. and up 10' to 16' 

Selects 1, IM, 1^, 2, 21^, 3&4in....8in. " 

Fine Common 1, 1^4, 1^^, 2, 2i^, 3 & 4 in. . ..6 in. " " 

No. 1 Cuts 1, 1M»1^, 2, 21^, 3& 4 in.... Miscellaneous " 

N0.2 " 1, 114, 11^ & 2 in " 

N0.3 " 1, li4,li^&2in '' 

No. 1 Moulding....!, 1^, 13^ & 2 in 4 to 9 in 

N0.2 " 1, 114, 11^^ & 2 in " 

Stained Saps 1, I14, IJ^ & 2 in " 

No. 1 Shelving 1 in 10, 12 & 13 in. and up. ** 

No. 1 Dressing 1, I14, 1)^ & 2 in Misc. and stock " 

No. 2 " ....1, 1)4, IV^, 2, 2j^&3in ** " '♦ 

Shaky Clear 1, 1)4, 1^, 2, 2i/>, 3 & 4 in.. . "- " '' »' 

Common 1, 1)4, 1)^, 2, 2)^, 3 & 4 in.... '* " '* " 



87a TIMBER. 

Terms Used. Thickness. "Widths. Lengrths. 

No. 1 Barn 1, 1^4, 1^^ & 2 in Stock widths 10' to 16' 

No.2 " " " " " " 

No.3 " '' " " " " 

Shippers 1 in 12 & 13 in. and up " 

Coffin Boards 1 in.. 13 in, and up " 

Box 1, 1^4, li/o, 2, 2]4&'i in Misc. and stock *' 

Mill Culls 1, 1^4, 11^ & 2 in Misc. and stock 



Synopsis of Buft'alo Grading*. 

F Uppers.— 10" and wider. 10" must be free from defects both 
sides. For every 2" in width over 10", defects may be allow^ed 
in the shape of one knot about the size of a nickel, or one half 
inch of bright sap on the back. No sap is allowed on the face of 
piece and no shake or rot. Very wide 2^, 3 and 4" uppers shipped 
may have a little shake at one end. 

Selects. — 8" and up. 8" must be clear both sides. For every 
2" over this wndth, defects allowed in the shape of one 1" knot or 
1" of bright sap on the back. In very wdde pieces very little 
bright sap may be allowed in face of addition. 

Fine Common. — 8" and up. An 8" piece may take 1" of bright 
sap on the back. A 10" piece may have as many as 3" of bright 
sap on the back, wider than 10" may have sap all over the back, 
provided it is bright, or corresponding defects in the shape of 
small knots in the middle of the piece. Wide, line common 
allows a small amount of fine shake on one end of the piece and 
on one side. Amount of shake, sap, and knots allow^able in a 
piece depends on the width and length. 

No. 1 Cuts.— 4" and up. Must cut | or better of all defects. 
Any kind of defect allow^ed, provided they will not interfere with 
cutting good lengths out of the piece between the defects. 

No. 2 Cuts.— 4" and up. Must cut | to f clear of all defect \ 

No. 3 Cuts. — Must cut 30 to 50 per cent clear of all defect;;. 

No. 4 Cuts.— Box lumber with knots scattered so as to allow 
short cuts between them. 

No.. 1 Moulding. — 4" and up. Must be clear of all defects 
on the face, a: d will allow any amount of bright sap on the back. 

No. 1 Siding Stuips.— Absohitdy free from defects both 
sides. Suitable for si.liltiug into bevel siding. 

15ahe and Casing Strips. — Take bright sap on both sides of 
piece and occasional small knots at the end of piece. A little 



TIMBER. Sib 

stained sap is allowed in this grade on back. Base is 8 and 10" 
wide, casing 5 and 6" wide. 

No. 2 Moulding and Stained Sap.— 4'' and up wide. Will 
allow any amount of bright sap or stained sap both sides, pro- 
vided the sap is not dozy. Will also allow some small knots in 
addition to sap. 

Shaky Clear. — 3" and up. Free of all defects on one face, 
saving a little bright sap and an occasional knot in wide pieces, 
and any amount of shake on the back, with as much sap and knots 
as allowed on the face. 

Dressing.— 4" and up wide. Allows any number of knots in 
the centre of the piece, provided they are sound, not larger than 
1" and not close enough together to interfere with the strength of 
the piece. No shake, rot, or stained sap. No knots allowed on 
the edges. 

Shelving. — The same as dressing, but 13'' and up wide. 

Shaky Dressing. — Is the same as the foregoing dressing, 4" 
and wider, and allowing in addition to the knots a fine shake on 
one or both sides. 

No. 1 Barn. — 4'' and up wide, allowing any number of red 
knots one side, provided they are no larger than 1\" and the twc 
edges on the face of the piece are free from knots. Branch kno/. 
allowed when small on the back, and the face if they do not rui_ 
to the edge. No shake or rot. Small amount of bright sap 
allowed. 

No. 2 Barn.— 4" and up wide. Will take any number of 
sound red knots, provided they will not break in matching. No 
shake, rot, or heart checks allowed. Bright sap allowed. 

No. 3 Barn. — 3" and up wide. Takes any number of coarse 
red knots and heart checks, if they do not interfere with the 
strength of the piece. 

Common. — Same as No. 1 and 2 Barn mixed would be. 

Box. — Will allow shake, black knots, and black sap, but must 
not extend over more than one half of the piece on both sides. 

Mill Culls. — All lumber which will not go in any of the 
above grades. 

Lath. — No. 1 should be clear. No. 2 will allow defects, but 
must be sound. 



87c TIMBER. 



Cypress— OflS-cial Classification. 

Tank Stock. — Shall be 5" and over in width. 1^" to 4" thick 
and 8' and over long. Pieces up to 7" shall be free of sap. 
Pieces wider than 1" may have 1" of sound sap on one edge, not 
to exceed half the length and half the thickness of the piece. In 
ill widths, sound kncts that do not impair its usefulness for tank 
purposes may be admitted. 

First and Second Clear. — Shall be 8'' and over in width. 
Pieces 8" to 10" may have V of bright sap on eachtedge, or its 
equivalent on one edge, otherwise they must be clear. Pieces 
10" and under 12" wide may have 1^" of bright sap on each edge, 
or 3" on one edge, and one standard knot 1|" in diameter. 

Pieces 12" wide may have one standard knot and 2" of bright 
sap on each edge, or the equivalent on one edge ; or in lieu of sap 
may have two standard knots or their equivalents. Pieces wider 
than 12" may admit of defects in proportion as width increases. 
Pieces 14" and wider may have one straight split not over 10" to 
12" long, when comparatively free from other defects. Slight 
season checks allowed in above grade. 

Selects. — Sliall have one face side and be 7" and over in width. 
Pieces 10" and under in width shall admit two standard knots 
of 1^" in diameter, and an additional standard knot for every 
two inches in width over 10". Bright sap not considered a 
defect. Unsound knots that do not go through the piece to be 
allowed. Pieces free from other defects, 10" and over wide, to 
admit pin-worm holes on one edge one tenth the width of the 
piece. Season checks, no defect. Slight wane on 10" pieces and 
over allowed on one side not over 3 feet in length. When no 
other defects appear, slight amount stained sap may be allowed. 
Pieces 10" and over in width may have a straight split not to 
exceed 12" in one end, when comparatively free from other 
defects. 

Shop.— Shop to be 6" and over in width, 8' and over in length, 
and to include all lumber that will not go into above grades, but 
that will cut for shop use 60 per cent clear of waste. 

Mekciiantable ok Common. — May be any width, admitting 
sap, knots, shake, or peck, when the strength is not impaired. 

Strips. — 4" to 6" strips shall be graded A, B, C, D, and read 
the same as flooring grades. 



TIMBER. Sid 

Siding.— '' Clear and A " siding may have 1" of bright sap on 
thin edge, and may contain one small sound knot. 

'' B " may have J of face bright sap if otherwise clear, or in 
lieu of i sap, may contain two small sound knots. 

" C " may be all bright sap or may have one to five knots, the 
whole not aggregating over 3'', or knots or other defects that can 
be removed in two cuts with waste not exceeding 12" in length, 
or three pin-worm holes, and may have check or split at one end, 
not exceeding 12" in length. 

"D'* may have stained sap and pin- worm holes, or may have 
other defects that will not cause a waste to exceed J the piece. 

Dressed Finishing. — Seven inches (7") and up random width 
to be two grades, as described in First and Second Clear and 
Select. 

Flooring, Ceiling, and Partition. — Clear must be free of 
sap and defects. 

*'A" may have 1" bright sap on one edge, may contain one 
small sound knot, or may have bright sap \ its width on one end 
for not exceeding 2 feet from end. 

*'B" may have \ of its face bright sap if otherwise clear, or 
in lieu of bright sap, contain two small sound knots, or may have 
a split not to exceed 9" at one end. 

*'C " may have all bright sap, or may have one to five knots, 
the whole not aggregating over 3", or knots or other defects that 
can be removed in two cuts, with waste not to exceed 12" in 
length, or may have three pin-worm holes, or may have check or 
split at one end, not to exceed 12" in length. 

' ' D " may have stained sap and pin-worm holes, or may have 
unsound knots or other defects that will not cause a waste to ex- 
ceed 1 of the piece. 

Dressed Finishing.— Strips 1", 1^', and 1^" x 4" to 6" wide 
to be graded as First and Second Clear and Select. The above 
First and Second Clear Strips, which are 1", 1\", and 1|" thick, 
shall have one heart face, and will admit one inch sap on one 
edge. Select may be all bright sap, or in lieu of sap may contain 
two standard knots. 2 X 4" and 2 X 6" to be graded Clear and 
Select, as described in above 1, 1\, and 1\" strips. 

Squares. — Squares to be graded Clear and Select 4 x 4" to 
10 X 10". A clear square to admit { its size of sap on one corner. 
Select may have half bright sap. 



ue 



TIMBER. 



Gauges for Matched Luniber. 

Flooring.— 1 X 4" and 1 X 6'' shall be f| x 3i" and || X SJ". 
1^" flooring shall be 1^". 

Ceiling.— f" shall be j%". f ' shall be //'. -| " shall be ^V'- 
I" shall be ^^", and the width shall be the same as flooring. 



Cypress Standard Diniensious. 

Manufacturers' Association List. 



Rough & Dressed Tank Stock. . .1J4'^ 
Firsts and Seconds 1'^ 

" m" 

'' 1^" 



Selects I" 

" W 

" 13^" 

" 2'' 

" 21^'' 

" 3'' 

Finishing & Strips, 1 x 4" and Q''. .A 

..B 
..C 
..D 

Lath, %" X 1)4" X 4' No. 1 

" %'' >< 13^" >^ 4' No. 1 

Battens, %'' x 3'', S. 1 S., 2 E. 
'' %" X 3", O. G. 
- 2", 

2^", ** 



Bevel Siding, 3^'^ x 6'', Clear and A 

B 

C 

D 

Ceiling, %'' x 4'' or 6'', Clear and A 

B 
C 
D 
" ]4'' ^ 4" or 6'', Clear and A 
B 
C 
D 
" %" X 4" or 6", Clear and A 

B 

C 

D 

' Clear & A 

Flooring, I " ^ 

Drop Siding, j ^ 

and %" Ceiling, J " D 

Pickets, 1^'^ X 114" X 4' No. 1 

N0.2 

%" X 2)4" x4' No. 1 

N0.2 

Car Roofing, V x Q" x 5' No. 1 

Car Siding, V x i'\ b'\ and 
Q" X 8' No. 1 



"j 4" or 6" ( 



88 TIMBER. 



Hardwood liUiiiber Grades. 

The Boston law for the inspection of black walnut and cherry, 
ash, oak, poplar, and butternut, requires that the woods be 
divided into three grades, number one, number two, and culls. 

Number One includes all boards, pLink, or joist that are free 
from rot and shakes, and nearly free from knots, sap, and bad 
taper ; the knots must be small and sound, and so few that they 
would not cause waste for the best kind of work. A split in a 
board or plank if parallel with the edge of a piece is classed 
number one. 

NuMBEii Two includes all other descriptions except when 
one third is worthless. When a board, plank, or joist contains 
sap, knots, splits, or any other imperfections combined, making 
jess than one third of a piece unfit for good work, and only fit 
for ordinary purposes, it is number two ; when one third is 
worthless it is a cull or refuse. 

Refuse or Cull hardwood includes all boards, planks, or 
joists that are manufactured badly, by being sawed in diamond- 
shape, smaller in one part than in another, split at both ends, or 
with splits not parallel, large and bad knots, worm-holes, sap, 
rot, shakes, or any imperfections which would cause a piece of 
lumber to be one third worthless or waste. 

All hardwoods are measured from six inches up ; and all lum- 
ber sawed thin is inspected the same as if of proper thickness, 
but is classed as thin, and sold at the price of thin lumber. 

The Regular Sizes are |-, 1-, 1J-, 1^-, 2-, 2^-, 3-, 4-inch, and 
up, by even inches. The regular lengths are 12, 14, and 16 feet ; 
shorter than 12 feet does not command full market price. 

Inspection of Quartered Oak and Yellow Pine. 

Oak for trimming, finishing, or flooring is rift-sawed ov quar- 
tered, that is, sawed with two cuts at right angles with each other, 
and through the centre of the log, all subsequent cuts being 
made as nearly as possible on radial lines. 

Oak is distinguished from all other woods by the ''silver 
grain " or medullary rays consisting of small bundles of fibres, 
which shoot out laterally from the centre of the trunk, passing 
through the annual rings toward the bark. By quartering the 
log these fibres are divided nearly or quite in the direction of 



TIMBER. 89 

their course, and show on the surface of the boards as flecks or 
irregular silvery streaks upon a ground of fine parallel lines 
formed by the section of the annual rings. If, on the contrary, 
the log is sawed into parallel slices in the ordinary manner, the 
middle slice will exhibit the silver grain, as will also one or two 
on each side of it. Further from the centre the medullary rays 
will be divided almost transversel3^ appearing on the cut surface 
as nearly imperceptible lines or dashes, while the sections of the 
annual rings will grow broader and broader, showing, since 
the sap tubes of oak are quite large, as a coarse, rough figure, 
completely different in appearance from the delicate and silvery 
grain, and liable to a dingy discoloration from the entrance of dust 
and dirt into the exposed pores. Some varieties of oak, sawed 
in the ordinary way, often appear hrashy, or of a very coarse tex- 
ture, with short fibres which break away easily. 

The manner in which the log is sawn affects also its disposition 
to warp and curl, which in badly cut oak is very strong. The 
inner portions of the tree are compressed and hardened by age, so 
that there is a gradual diminution of density toward the circum- 
ference, which is occupied by the soft and spongy sap-wood. The 
less compact substance naturally shrinks more in drying than 
that which is nearer the interior of the log, but with boards 
whose surfaces follow the radial lines the movements caused by 
dryness or damp are all in the planes of these surfaces, and 
although the board varies in width, it has no tendency to warp. 
Those boards, on the contrary, which are cut in lines parallel with 
the diameter of the log have one surface which looks toward the 
bark of the tree and the other toward the heart, and the fibres 
on one side are therefore slightly softer than on the other, and 
will shrink more, curling the piece outward with a force proper- 
tioned to its thickness. 

By keeping constantly in mind these properties of oak, which 
belong in some degree to all kinds of timber, many annoying de- 
fects in hardwood finish may be avoided. 

Yellow Pine for floors and finishing is cut, like quartered oak, 
on radial lines. These may be recognized by the figure, consist- 
ing of fine parallel lines in place of the broad mottlings produced 
by a cut tangent to the annual rings. Hard-pine boards of the 
latter kind are very liable to splinter and must be rejected. Hard- 
pine boards containing large streaks of dark turpentine should be 
rejected, as Ithe turpentine soon crumbles away. 



90 METALS. — IRON. 



VI. Metals. 



The metals used in construction are iron, copper, lead, tin, 
zinc, and some of their alloys. 

These metals are not found to any great extent in the pure 
metjillic state, but chiefly in the form of oxides, carbonates, or 
sulphides called '* ores." 

The ores are broken up, and separated from the earthy matters 
adhering to them, by stamping or crushing in mills and by wash- 
ing with a stream of water, which carries away the lighter im- 
purities, leaving the ore, which is then said to be ''dressed." 

The extraction of the metal from the ore is effected by various 
processes, generally by smelting, the ore being mixed with a flux ; 
i.e., a mineral substance which will readily combine with the im- 
purities of the ore is placed in a suitable furnace and subjected 
to intense heat, upon which the metal sinks down in a fluid 
state, while the impurities combine with the flux and run off in a 
light and fusible slag. 

Iron. 

Iron is extracted from its ores by smelting in a blast-furnace, 
using either a " cold blast," i. e., a blast at ordinary temperature, 
or a *'hot blast." In this the air is raised to a temperature 
of from 800° to 1400° F. before being forced into the furnace. 
The intense heat developed causes fusion of the substances. 
The molten metal sinks to the bottom and over this is collected 
a glassy refuse composed of the lighter and more fusible im- 
purities. This is called " slag." The slag is drawn off, run into 
iron cars, and haided to the dumping-ground. 

When a considerable quantity of molten iron has collected the 
furiuice is tapped, and the iron is run into a long channel formed 
in sand, having smaller channels on each side. These small 
channels are 3 or 4 inches deep and 2 to 2| feet long. The 
channels are called the sow and her pigs; hence the bars produced 
are called " i)ig iron." 

It is generally considered that the cold-blast irons are superior 
to the hot-blast. The hot bhist, while saving fuel and producing 
a larg(jr yield, also causes the iron to combine with a larger 
quantity of impurities. 



METALS.— PIG IRON. 



91 



Pig Iron is classed under several heads, as Foundry Pig, 
Bessemer Pig, and Forge Pig, These classes are graded according 
to the character of the fracture, the number of grades varying in 
different localities. In Eastern Pennsylvania the principal grades 
recognized are known as No. 1 and No. 2 Foundry, No. 3 Qray 
Forge, No. 4 Mottled, and No. 5 White. Intermediate grades are 
sometimes made, as No. 2X between No. 1 aud No. 2, and special 
names are given to irons more highly silicized than No. 1, as 
No. IX, Silver Gray, and Soft. Charcoal foundry pig iron is 
graded by numbers 1 to 5, but the quality is very different from 
the corresponding numbers in anthracite and coke pig. Souihern 
coke pig iron is graded into ten or more grades, as follows, 
beginning with the highest in silicon: Nos. 1 and 2 Silv ry, Nos. 1 
md 2 Soft, all containing over 8 per cent of silicon; Nos. 1, 2, and 
3 Foundry, respectively about 2.75 per cent, 2,5 per cent, and 2 
per cent silicon; No. 1 Mill, or Foundry Forge, No. 2, or Gray 
Forge; mottled, and white. 

Table 8. 

COMPOSITION OF PIG IRON. 

The following analyses show the composition of the five stand- 
ard grades of Northern foundry and mill pig irons: 



Iron 

Graphitic carbon 

Combined carbon... 

Silicon 

Phosphorus 

Sulphur 

Manganese 



No. 1 
Gray. 



92.37 

3.52 

.13 

2.44 

1.25 

.02 

.28 



No. 2 
Gray. 



92.31 

2.99 

.37 

2.52 

1.08 

.02 

.72 



Used exclusively 
in the foundry. 



No. 3 
Gray. 



94.66 
2.50 
1.52 
.72 
.26 
trace 
.34 
Rolling- 
mill or 
foundry. 



No. 4 
Mottled. 


No. 4 B. 


94.48 


94.08 


2.02 


2.02 


1.98 


1.43 


.56 


.92 


.19 


.04 


.08 


.04 


.67 


2.02 



No. 5 
V^hite. 



94.68 

*3;83 
.41 
.04 
.02 
.98 



Rolling-mill. 



Impurities in Pig iron. 

The various ores and the mineral fuels used in smelting fre- 
quently contain substances which injure the quality of the respec- 
tive metals produced from the pig iron unless eliminated in sub- 
sequent processes. 

The following are some of the princii)al impurities: 



92 METALS. — PIG IKON. 

Phosphorus is very readily taken up during the smelting 
process, and is one of the worst impurities it can contain. 

Cast iron is hardened by it, but is made more readily fusible; 
shrinkage is decreased and fluidity increased. Its tenacity is 
reduced. 

Wrought iron is injured by it in proportion to the quantity 
present. 

yV per cent does not reduce the strength, but improves its 
welding capacity. 

Y% per cent makes it harder, but not weaker. 

j% per cent makes it " cold-short." 

1 per cent makes it very brittle, and unfit for any but special 
purposes. 

Steel is injured by a very minute proportion. 

Sulphur is derived from the pyrites in the ore and coal. 

In cast iron it tends to produce the mottled and white varie- 
ties; in general its influence is to drive out carbon and silicon, to 
increase chill and shrinkage, and to decrease strength. 

In icrouglit iron three tenths per cent produces *' Red-short- 
ness. 

In steel one tenth per cent produces *' Red-shortness"; more 
than two tenths per cent unfits it for forging, but makes it more 
fluid. 

Manganese. In cast iron it tends to produce the white variety; 
it increases the holding capacity for carbon, reduces plasticity, 
and increases brittleness and shrinkage. 

Manganese decreases the magnetism of iron. This character- 
istic increases with the percentage present. When 25 per cent is 
present the iron loses all its magnetism. This peculiarity has 
been made use of by French metallurgists to draw a clear line 
between spiegel and /(^rrt?- manganese. When the pig iron con- 
tains less than 25 per cent of manganese it is classed as spiegel, 
and when more than 25 per cent it is classified as ferro-manga- 
71686. For this reason manganese iron has to be avoided in cast- 
ings of dynamo-fields and other pieces belonging to electric 
machinery. 

When the quantity of manganese is under 40 per cent, with 
tlie remainder mostly iron, and silicon not over 0.50 per cent, the 
alloy is called Spiegeleisen, and the fracture will show flat reflect- 
ing surfaces, from which it takes its name, 

A liltle manganese is an e.Xfellent antidote against sulphur in 
the furnace. 



METALS.-— PIG IROK. 93 

In lorougld iron and steel it counteracts red-shortness. Its 
presence is esseutial in the maiiufncture of Bessemer steel, and in 
some other processes. 

Silicon. — The effect produced by silicon in cast iron varies 
according to the physical properties of the original iron: in some 
it causes hardness and brittleness, and decreases shrinkage; a 
small percentage usually increases strength, high percentage de- 
creases strength. 

Wrought iron is rendered by it hard and brittle. To obtain 
good wrought iron the silicon must be removed as far as possible 
by repeatedly heating and working the iron. 

Steel. — 2 0^0 part makes it cool and solidify without bubbling 
and agitation, more makes it brittle ; ^ per cent makes it uu- 
forgeable. 

Materials Produced from Pig Iron. 

By subjecting pig iron to various processes three varieties of 
material are produced, viz.: Cast Iron, AVrought Iron, Steel. 

The great differences that exist between these materials depend 
chiefly upon the amount of carbon they respectively contain, the 
other substances present being generally regarded as impurities. 

The percentage of carbon present in these materials and their 
several gradations is about as follows: 

Cast iron 4.00 to 5.00 per cent. 

Malleable cast iron 0.88 *' 1.53 *' 

Wrought iron 0.00'' 0.25 *' 

Soft steel 0.075 " 

Mildsteel 0.08" 0.20 '* 

Hard steel 0.20'' 0.40 " 

Tool steel 0.40" 0.80 '* 

Draw-plate steel 3.30 " 



94 METALS. — CAST IRON". 



Cast Iron. 



Cast iron is obtained by remelting the foundry pig iron and 
running it into moulds of the shape required. 

Ill some cases the metal is run into the moulds direct from the 
blast-furnace, but in superior work it is generally specified that 
the cast iron is to be of the '* second melting," ♦Jiat is, from pigs 
remelted in a cupola. 

There are two principal varieties of cast iron, the gray and the 
iMte, differing in their chemical and physical characters ; and 
between these two are several intermediate varieties, which re- 
semble more or less the gray or the white as they approach 
nearer to one or the other. 

Gray iron contains one per cent or less of carbon chemically 
combined, and from one to four per cent of carbon in the state of 
graphite mechanically mixed. 

The gray iron is soft and tough, slightly malleable when cold, 
may be drilled, planed, or turned, melts at a lower heat than the 
white, being red when molten, remains fluid a long time, fills the 
mould readily, and gives tine sharp angles to the casting. The 
fracture is granular, of a gray color, with a metallic lustre. 

^^hiie iron contains from two to five per cent of carbon in a 
state of chemical combination. It is hard, brittle, and sonorous, 
cannot be worked, is not easily melted, is white when fluid, 
thickens rapidly, and shows a white crystalline fracture, with a 
vitreous lustre. 

The gray iron is most suitable for strength, the white for hard- 
nes«. 

The two varieties may be produced from the same ore under 
different conditions of temperature. The carbon requires to cool 
slowly in order to form graphite, and to exist as a separate mate- 
rial in the iron ; rapidly cooled, the carbon remains chemically 
combined, thus producing white iron. 

The term " chilling" irons is generally applied to those which 
if cooled slowly would be gray, but when cooled suddenly become 
white either to a depth sufiicient for practical utilization (e. g., in 
car- wheels) or so far as to be detrimental. Many irons chill more 
or less in contact with the cold surface of the moulds in which 
they are cast, especially if they are thin. Sometimes this is a 
val«iR))le quality, but for general foundry purposes it is desirable 
10 have all parts of a casting an even gray. 



METALS. — OAST IROK". 96 

The density and strength of cast iron is increased by repeated 
remeltlug up to about the twelfth time, after which it is decreased. 
The increase is the result of the gradual abstraction of the con- 
stituent carbon and the consequent approximation to wrought 
iron. 

By prolonged fusion the tenacity is increased. 

Both remeliing and prolonged fusion may be carried too far; 
as the carbon is removed the iron becomes less fluid, fills the 
moulds less perfectly, and produces too hard and brittle a metal. 



Properties of Cast Iron. 

Specific Gravity, 6.85 to 7.48. 

Weight per Cubic Foot, usually assumed at 450 lbs. 

Atomic Weight, 56. 

Hardiness, 4.57 to 33.51. 

Melting-point: Gray iron, 2012° to 2786° F. 
White iron, 1922° to 2075° F. 

Specific Heat, .1298. 

Conductivity for Heat, 11.9. 

Conductivity for Electricity, 12 to 14.8 (silver being 100). 

Expansion and Contraction. — Expansion in bulk by heat, 
.0033 ; exposed to continued heat it becomes permanently ex- 
panded from 1| to 3 per cent of its length. A bar will contract 
or expand .000006173 of an inch, or xeAn^ ^^ i^^ length for 
each degree of heat ; between the extremes — 20° F. and + 120° 
F. it will contract or expand .0008642 of an inch, or the 1157th 
part of its length, equivalent to a strain of 4| tons per square 
inch. 

Contraction on cooling ranges from ^^^h to ^^^th of the 
length. 

Extension, ^^^V^ of its length per ton per square inch, or 
.000000107 of its length per pound of tension. 

Compression per pound = .0000000804 of the length. 

Elongation. — The elastic limit is not clearly defined, the 
elongation increasing faster than the increase of the loads from 
the beginning of the test. The modulus of elasticity is therefore 
variable, decreasing as the loads increase. The following results 
of a test by Prof. Lanza are an example ; 



96 



METALS. — CAST IRON. 



Table 9. 

CAST IRON: ELONGATION AND MODULUS OF ELASTICITY. 



Pounds per 


Elongation in 


Sets in 


Modulus of 


Square Inch. 


13.4 inches. 


Elasticity. 


1000 


.0004 




18,217,400 


2000 


.0013 




16,777,700 


3000 


.0024 




14,085,400 


4000 


.0036 




18,101,200 


5000 


.0048 




12.809,200 


6000 


.0061 


.6066 


12,319,300 


8000 


.0088 


.0001 


11,600,800 


10000 


.0119 


.0001 


10,930,500 


12000 


.016 


.0007 


9,714,200 



Shrinkage. — The usual allowance for shrinkage is J inch per 
foot. 
Ultimate Strength.— Tensile, 9000 to 45.970 lbs. per sq. in. 
Compressive, 80,000 to 174,120 lbs. per 

sq. in. 
Shearing (mean), 24,000 lbs. per sq. in. 
Torsion " 8,614 " *' 

Transverse, 500 to 4,000 '* *' 
Working Strength. — Tensile, 3,000 lbs. per sq. in. 

Compressive, 80,000 " " 
Transverse, 600 " ** 

Shearing, 6,000 " *' 

Torsion, 5,000 '' '* 

Tenacity at High Temperatures. — Cast iron appears to 
maintain its strength, with a tendency to increase until 900° F. is 
reached, beyond which temperature it gradually decreases. (Jas. 
E. Howard's Tests, Iron Age, April 10, 1890.) 

Cast iron of averaeje quality loses strength when heated above 
120° F. ; and it becomes insecure at the freezing-point. At a red 
heat its normal strength is reduced one third. (D. K. Clark.) 



METALS.— CAST IRON. 97 



Notes on Founding. 

Cast iron becomes more compact and sound by being cast 
under pressure ; hence pipes, columns, and the like are stronger 
when cast in a vertical than in a horizontal position, and stronger 
still when provided with a head, or additional column of iron, 
whose weight serves to compress the mass of iron in the mould 
below it. The air-bubbles ascend and collect in the liead, which 
is broken off when the casting is cool. 

** Blow-holes" and ''honeycomb" are produced by confined 
air and render castings defective. 

Cavities and flaws caused by unequal contraction during cool- 
ing, and the collection of foundry dirt and other impurities, are 
frequent sources of weakness. 

In column and pipe castings a common defect is unevenness of 
thickness. This may be detected either by drilling small holes 
along the sides, or by a careful application of the calipers. If 
one side is much thicker than the other the thin side cools first 
and is consequently subjected, during the cooling of the thick 
side, to strains frequently severe enough to bend the casting and 
produce injury. Columns or pipes cast upon their sides suffer 
from this imperfection by the displacement of the core. Columns 
or pipes taken from the mould too quickly are apt to be bent in 
the handling. 

Unequal contraction of the metal in cooling frequently causes 
strains which produce rupture especially in columns and lug 
castings. 

When castings are of such length as to make it necessary to 
pour the metal into the mould from both ends, it frequently 
occurs that the iron becomes too much chilled to properly mix 
and unite, thus forming weak seams, called ** cold-shuts." 

Castings should be covered up and allowed to cool as slowly as 
possible. They should remain in the sand until cool. If they are 
removed from the mould in a red-hot state, the metal is liable to 
injury from too rapid and irregular cooling. 

The unequal cooling and consequent injury caused by great 
and sudden differences in the thickness of parts of a casting are 
sometimes avoided by uncovering the thick parts so that they 
may cool more quickly. 



98 METALS. — CAST IROK. 

Inspection of Cast Iron. 

The appearance of good cast iron for structural purposes 
should show on the outer surface a smooth, clear, and continuous 
skin, with regular face and sharp angles. When broken, the 
surface of the fracture should be of a light bluish-gray color and 
close-grained texture, with considerable metallic lustre ; both 
color and texture should be uniform, except that near the skin 
the color may be somewhat lighter and the grain closer; if the 
fractured surface is mottled, either with patches of darker or 
lighter iron, or with crystalline patches, the casting will be un- 
safe, and it will be still more unsafe if it contains air-bubbles. 
The iron should be soft enough to be slightly indented by a blow 
of a hammer on the edge of the casting; if it is hard and brittle, 
fragments will be broken off. 

Castings are tested for "honeycomb" by tapping with a 
hammer. 

Blow- or sand-holes filled in with sand from the mould or 
purposely stopped with loam cause a dulness in the sound which 
leads to their detection. 

In examining water-pipes and the castings connected therewith, 
see that the interior is free from swells, scale, and blisters. Test 
thickness with the calipers. Sound thoroughly with the hammer 
to discover flaws, air- or sand-holes. Examine the junction of the 
hubs or bells with t"he body for honeycomb. See that the hydraulic 
pressure required by the specifications is applied. While under 
pressure tap the pipe all over to discover flaws, etc. Inspect 
the weighing and marking of each piece. 

Columns and posts are examined for cold-shuts, sand- and blow- 
holes; the thickness of the shaft in closed columns is tested by 
drilling a sufiicient number of f-in. holes. The connections of 
lugs, brackets, capitals and bases require close examination to 
discover flaws, shrinkage cracks and blow-holes. 

Test Bars.— The test-bars should be poured alternately before 
and after the casting is poured; there should be at least one test 
bar for each 2000 lbs. of castings, or sucb number as the specifica- 
tions require. 

The test-bars are usually 3 in. wiae by 1 in. thick, and either 14 
or 20 in. long; they are placed on supports 12 or 24 in. apart, 
narrow side up, and loaded in the centre until broken. Note the 
deflection and breaking weight. 

The b.'irs for ttsling tensile strength are usually turned down 
on a lathe in order to remove the rough exterior scalii and enable 
the diameter to be carefully measured. 



METALS.— CAST IRON. 



99 



Table 10. 

CAST IRON. WEIGHT OF PLATES, ROUND AND SQUARE BARS. 



CO V . 

m 

o 


ill 




t^ tub 


^11 


o 


CO O 

H 


42 

si. 


4 

U2 


^3 bl 

^M o 

^1! 


Wt. of a 

Round Bar 

1 Foot Long. 


02 

i 

o 




ft 


Lbs. 


Lbs. 


Lbs. 


Lbs. 


s 


Lbs. 


Lbs. 


Lbs. 


Lbs. 


1/32 


.0026 


1.173 


.003 


.002 




'^Vs 


.2604 


117.3 


30.52 


23.97 


4.162 


1/16 


.0052 


2.344 


.012 


.010 






.2708 


121.8 


33.01 


25.93 


4.681 


3/32 


.0078 


3.516 


.027 


.021 


.OOOll 


&/. 


.2813 


126.5 


35.60 


27.95 


5.243 


Vh 


.0104 


4.687 


.048 


.038 


.0003 


1^ 


.2917 


131.2 


38.28 


30.07 


5.846 


5/32 


.0130 


5.861 


.076 


.060 


.0005' 


% 


.3021 


135.9 


41.07 


32.25 


6.498 


3/16 


.0156 


7.032 


.110 


.086 


.0009, 


% 


.3125 


140.6 


43. sn 


34.51 


7.193 


7/32 


.0182 


8.203 


.150 


.118 


.0014 


Vs 


.3229 


145.3 


46.9: 


36.85 


7.934 


M 


.0208 


9.375 


.195 


.154 


.00211 


4 


.3333 


150.0 


50.01 


39.27 


8.726 


9/32 


•0234 


10.54 


.247 


.194 


.0030 


^ 


.3438 


154.7 


53.18 


41.77 


9.572 


5/16 


.0260 


11.73 


.305 


.240 


.0042 


34 


.3542 


159.3 


56. 4t) 


44.33 


10.47 


11/32 


.0287 


12.89 


.370 


.290 


.0056 


% 


.3646 


164.0 


59.82 


46.99 


11.42 


ak 


.0313 


14.06 


.440 


.346 


.0072 




.3750 


168.7 


63.33 


49.71 


12.43 


13/32 


.0339 


15.24 


.516 


.400 


.0092' 


52 


.3854 


173.4 


66.86 


.52.52 


13.49 


7/16 


.0365 


16.41 


.598 


.470 


.0114; 


M 


.3958 


178.1 


70.52 


55.39 


14.62 


15/32 


.0391 


17.56 


.687 


.540 


.0140: 


% 


.4063 


182.8 


74.28 


58.34 


15.81 


^ 


.0417 


18.75 


.781 


.610 


.0170! 


5 


.4167 


187.5 


78.12 


61.37 


17.05 


9/16 


.0469 


21.10 


.989 


.777 


.0243; 




.4271 


192.2 


82.10 


64.47 


18.35 


% 


.0521 


23.44 


1.221 


.959 


.0334! 


34 


.4375 


196.9 


86.14 


67.65 


19.73 


11/16 


.0573 


25.79 


1.478 


1.161 


.04441 




.4479 


201.6 


90.29 


70.52 


21.18 


H 


.0625 


28.12 


1.758 


1.381 


.0575 


1^ 


.4583 


206.2 


94.54 


74.26 


22.68 


13/16 


.0677 


30.47 


2.064 


1.621 


.0732 


% 


.4688 


210.9 


98.89 


77.66 


24.27 


% 


.0729 


32.81 


2.393 


1.880 


.0913 


M 


.4792 


215.6 


103.3 


81.16 


25.93 


15/16 


.0781 


35.16 


2.747 


2.158 


.1124 


% 


.4896 


220.3 


107.9 


84.72 


27.41 


1 


.0833 


37.50 


3.125 


2.455 


.1863 


6 


.5000 


225.0 


112.5 


88.36 


29.44 


1/16 


.0885 


39.84 


3.528 


2.771 


.1636 


34 


.5208 


234.4 


122.1 


95.89 


33.28 


Vs 


.0938 


42.19 


3.955 


. 3.107 


.1942 


4 


.5417 


243.8 


132.0 


103.7 


37.44 


3/16 


.0990 


44.53 


4.407 


3.461 


.2284 


H 


.5625 


253.1 


142.4 


111.9 


41.94 


M 


.1042 


46.87 


4.883 


3.835 


.2664 


7 


.5833 


262.5 


153.2 


120.2 


46. :7 


5/16 


.1094 


49.22 


5.384 


4.229 


.3084 


34 


.6042 


271.9 


164.2 


129.0 


51.97 


% 


.1146 


51.57 


5.909 


4.640 


.3546 


^ 


.6250 


281.3 


175.8 


138.1 


57.54 


7/16 


.1198 


53.91 


6.461 


5.073 


.4058 


% 


.6458 


290.7 


187.7 


147.4 


63.47 


3^ 


.1250 


56.26 


7.033 


5.523 


.4603 


8 


.6667 


300.0 


200.1 


157.0 


69.82 


9/16 


.1302 


58.60 


7.632 


5.993 


.5204 


M 


.6875 


309.4 


212.7 


167.0 


76.58 


Vs 


.1354 


60.94 


8.253 


6.484 


.5852 




.7083 


318.8 


225.8 


177.3 


83.74 


11/16 


.1406 


63.28 


8.900 


6.991 


.6555 


M 


.7292 


328. 2 


239.3 


187.9 


91.35 


% 


.1458 


65.63 


9.572 


7.518 


.7310 


9 


.7500 


337.4 


253.1 


198.8 


99.42 


13/16 


.1510 


67.97 


10.27 


8.064 


.8122 


/4 


.7708 


346.8 


267.4 


210.0 


107.9 


% 


.1563 


70.32 


10.99 


8.630 


.8991 




.7917 


356.2 


282.1 


221.5 


116.8 


15/16 


.1615 


72.66 


11.73 


9.215 


.9920 


% 


.8125 


305.6 


297.0 


233.3 


126.3 


2 


.1667 


75.01 


12.50 


9.821 


1.073 


10 


.8338 


375.0 


312.5 


245.5 


136.3 


/^ 


.1771 


79.70 


14.11 


11.09 


1.308 


M 


.8542 


381.4 


328.4 


257.8 


146.8 


M 


.1875 


84.40 


15.83 


12.43 


1.554 


3^ 


.8750 


393.7 


344.5 


270.6 


157.9 


% 


.1979 


89.07 


17.63 


13.85 


1.827 


4 


.8958 


403.1 


361.2 


283.7 


169.3 


% 


.2083 


93.75 


19.54 


15.34 


2.131 


11 


.9167 


412.5 


378.2 


297.0 


181.5 


.2188 


98.44 


21.54 


16.56 


2.467 


H 


.9375 


421.9 


395.5 


310.6 


194.2 


^ 


.2292 


103.2 


23.64 


18.56 


2.835 




.9583 


431.2 


413.3 


324.6 


207.3 


% 


.2396 


107.8 


25.84 


20.29 


3.241 


% 


.9792 


440.6 


431.4 


338.8 


219.2 


3 


.2500 


112.6 


28.13 


22.10 


3.682 


12 


iFoot 


4r)0.0 


450.0 


353.4 


235.6 



At 450 lbs. per cubic foot a pound contains 3.84 cubic inches, a ton 5 cubic 
feet, an<J a cubic inch weighs .2604 lb, 

UofC. 



100 METALS. — CAST IRON. 



Malleable Cast Iron. 

Malleable cast iron is the name given to castings made of 
ordinary cast iron which have been subjected to a process of de- 
carbonization, which results in the production of a crude wrought 
iron. 

The castings are made in the usual way, and are then em- 
bedded in oxide of iron, usually of hematite ore, or in peroxide 
of manganese, and exposed to a full red heat for a sufficient 
length of time to insure the nearly complete removal of the 
carbon. This decarbonization is conducted in cast-iron boxes, 
in which the articles, if small, are packed in alternate layers with 
the decarbonizing material. The largest pieces require the long- 
est time. The fire is quickly raised to the maximum tempera- 
ture, but at the close of the process the furnace is cooled very 
slowly. The operation requires from three to five days with 
small castings, and may take two weeks for large pieces. 

Strength of Malleable Cast Iron. 

Tensile— 25,000 to 50,000 lbs. per square inch. 
Elongation — 1 to 2 per cent in 4 inches. 
Elastic Limit— 15,000 to 21,000. 

Inspection of Malleable Iron Castings. 

The fracture should be fine-grained and uniform, and be free 
from blow^-hoies ; the centre should appear almost as dark as 
burnt iron. 

Tests should be made at the foundry prior to shipment, extra 
ca-tings from which to cut test pieces being furnished at the rate 
of at least two for every 2000 lbs. of product. 

All test-pieces should be cut, prepared, and tested under the 
eye of tlie inspector. 

Sbould the average of three tests show a less strength than 
required by the specifications, a repetition of the tests will be at 
the option of the inspector. 

Each casting requires to be closely examined for shrinkage 
cracks, blow-holes, large ridges ut partings, and flaws on edges, 
(.'astiiigs that are incorrect in dimensions or warped should be 
rejected. 



METALS. — OAST IRON". 100a 

Specifications for Malleable Iron Castinj»s. 

Tensile Requirements. — At the option of the inspector, 
one, two, or three castings of either the same or diflCerent pat- 
terns shall be selected from each 2000 pounds of finished product. 
From one or all of the castings thus selected test pieces shall be 
cut and prepared ; one from each selected casting. The position 
in the casting from which the test piece shall be cut is to be de- 
termined by the inspector. The size of the test piece shall be as 
nearly as possible, such as will give, when the piece is prepared, 
a uniform clear length of 4 inches between the grips of the testing 
machine, and such as will give, as nearly as possible, a cross- 
section area of | square inch. Tests of one or each of the pieces 
thus prepared shall show a tensile strength of not less than 
40,000 pounds and not more than 47, 000 pounds per square inch. 
The elongation and reduction of area measured after fracture 
shall be distinctly noticeable as indicatiDg some degree of duc- 
tility, and should be at least 1.5 per cent for each. Should the 
average of three tests show a tensile strength below 43,000 
pounds, and coupled with this if ductility is not plainly discerni- 
ble, the inspector shall have the option of repeatiog the test. 

Transverse Requirements. — Besides the tensile tests, trans- 
verse tests shall be made as follows : From the same castings, or 
others, at the option of the inspector, one, two, or three test 
pieces shall be prepared, giving a length of 12 inches between 
centres of supports and having as nearly as possible a cross- 
section of 1 square inch. If there should be any difference in 
the dimensions of the sides, the piece should be set in the 
machine with the greatest dimension vertical. 

The supports shall be 12 inches apart, centre to centre, and of 
the usual shape for making transverse tests of gray-iron castings. 
Test of one or each of the test pieces thus prepared shall show 
an ultimate tensile transverse strength of from 3900 to 4800 
pounds per square inch, and deflections from 0.35 to 0.65 inch. 
The average breaking load for any number of tests should be 
about 4900 pounds per square inch, and the average deflection 
about 1.5 inch ; this for specimens of the sizes recommended and 
for a metal of the characteristics suitable for car-castings. 

The fractures in both tensile and transverse tests should be 
fine grained and uniform ; blow-holes should be absent ; bright 
edges like the chill in chilled castings should generally show dis- 
tinctly at the edges ; the centre should generally appear almost 



lOOb METALS.— CAST IRON. 

as dark as burnt iron. No great dependence, however, can be 
put upon an examination of the fracture in determining the 
quality of malleable castings, further than seeing that castings 
are of uniform fine grain and free from blow-holes, as the frac- 
ture will vary in appearance according to the size of section. 

Bending and Torsional Tests. — Malleable castings which 
successfully pass the above requirements in tensional and trans- 
verse tests will generally successfully pass bending and torsional 
tests of equivalent severity. Reasonably thin sections, about 
8/lG to 9/16 inch thick, by about 1 to 3 inches wide, should bend 
over on themselves around a circle at the bend equal in diameter 
to twice the thickness of the piece and back again straight. 
And in torsion a thin piece of uniform dimensions, or nearly so, 
should twist once around without fracture. It only requires 
proper mixtures and proper annealing, coupled with care in other 
particulars, to make malleable castings that will weld on them- 
selves ; that will draw out to a knife-edge on an anvil under a 
hammer ; that will temper and cut soft iron like a cold chisel. 

Notes and Instructions to Inspectors. — All tests should 
be made at the place of manufacture prior to the shipment of 
the castings. Extra castings from which to cut test pieces or 
test pieces cast in moulds, and the preparation of test pieces, shall 
be made at the expense of the manufacturers. Test pieces cast 
in moulds are to be furnished if required. If manufacturers 
have no means of making tests, the expense of making tests 
elsewhere shall be borne equally by manufacturer and purchaser. 
Planed and turned test pieces should be tested occasionally to 
determine the i^enetrative effect of annealing. The effect of 
suddenly applied loads corresponding to shocks should be deter- 
mined by some convenient tests. In car-load shipments the 
inspector is to determine whether but three test pieces shall rep- 
resent the car-load. If a car-load is made up of such a great 
variety of patterns as not to be fairly represented by three test 
pieces, and if there is any doubt in the mind of the inspector as 
to the uniformity of product in the car-lead lot, he shall test 
enouirli ]>ieces to represent fairly the whole lot. It is almost 
impossible, from the limited amount of information on the sub- 
ject of malleable castings, to determine upon requirements in 
bending and torsional tests. It is quite certain that one set of 
requirements will not do for general car and locomotive machine 
and agricultural castings. If )\atterns two furnished by manu- 



METALS. — CAST IRON. lOOc 

facturers, inspectors shall insist that all abrupt changes in forms 
shall be relieved by fillets. In case of duplicate patterns, cast- 
ings from same shall compare closely in weight. All castings 
shall compare closely with guaranteed weights when in compe- 
tition with gray-iron castings^ Besides making tensile and other 
tests, inspectors shall closely inspect all castings, rejecting all 
that show unmistakable defects, such as shrinkage cracks, large 
ridges a' partings, [evidence of blow-holes, castings badly warped, 
cracked or broken castings, castings not properly cleaned, cast- 
ings that are incorrect in important dimensions due to errors in 
patterns, castings requiring cleaning, pickling, or machining 
not previously agreed upon. 



METALS.— WKOUGHT lUOl^. 101 

Wrought Iron. 

Wrought iron in its perfect condition is simply pure iron It 
falls short of that perfect condition to a greater or less extent 
owing to the presence of impurities. 

Wrought iron may be produced direct from the ore but is 

commonly obtained from /(>7•^6^^^ or the harder varieties of piff 
iron. ^ ^ 

In the manufacture of -refined iron" or - merchant-bar 
iron," the object to be attained is the removal of the carbon, phos- 
phorus, silicon, and other impurities. 
The refining process is performed as follows : 
I. PuDDLiNa.— The pig iron mixed with oxidizing substances 
such as hematite ore, limestone, salt, etc., is placed in a rever' 
beratory furnace and melted, the molten metal being stirred and 
agitated with a rake or - rabble." The admission of air during the 
stirring oxidizes the carbon and silicon, which pass ojff in the slag 
As the iron becomes purer it becomes less fusible and stiffens It 
is then worked by the puddler into lumps or balls cMed puddle, 
balls or blooms, weighing about 75 lbs. each. These balls are re- 
moved from the furnace and placed either under a tilt-hammer or 
squeezer to be shingled, that is, to have the cinder forced out and 
to be formed into suitable shape for rolling into muck-bars 

II. Rolling Muck-bars. -The shingled iron is next passed 
through the muck rolls and reduced to bars from 3 to 4 in wide 
f to 1 in^thick, and 10 to 12 ft. long, and very rough in appear' 
ance. These constitute what are known as - muck-bars " or 
" puddled bars," or the lowest grade of iron. 

The muck-bars are cut up into lengths of 6 or 7 ft., depending 
upon the size of the piece to be rolled, placed in an oven with 
waste scrap, reheated, and passed through the rolls. The bars so 
produced are called refined iron. 

For Double defined Iron the bars of refined iron are cut up 
piled, reheated, and again rolled into llat bars. These are repiled 
and rolled into final shapes. This iron is much stronger and more 
homogeneous than ordinary refined iron. 

After the iron is rolled to final shape it is run out on a series of 
skids called the hot-bed, where it is allowed to cool. From here 
It goes to the straightening-machine. This may either be a gag- 
press or a train of rolls, three below and two above. The latter 
IS much the better, producing straighter bars with less iniury to 
the material. ** ^ 



102 



METALS. — WROUGHT IRON. 



Tiie iK'aling aud rolling several times improves the quality of 
the iron, but it will Dot stand too many. The fifth reheating 
seeuis to be the limit. 

After coming from the straightening-rolls the material is 
luarked aud sheared, then inspected, aud each piece marked with 
its true dimensions in white-lead paint. 

Wrought iron is distinguished from the other varieties of iron 
by the property of welding; two pieces, if raised nearly to a white 
heat }ind pressed or hammered firmly together, adhere so as to 
form one piece. In all operations of rolling or forging iron of 
which welding forms a part, it is essential that the surfaces to be 
welded should be brought into close contact, and should be per- 
fectly clean and free from oxide of iron, cinder, and all foreign 
matter. 

Table 11. 

COMPOSITION OF WROUGHT IRON. 

The following analyses show the composition of some standard 
brands of wrought iron . 



Sulphur 

Phosphoius 

Silicon . 

Carbon . 

Manganese . . . 

Slag 

Tensile strength 



trace 
0.084 
0.105 
0.512 
0.0-.^9 
0.452 
66.598 



0.001 
0.035 
0.028 
0.066 
0.009 
1.214 
54.363 



III. 



0.008 
0.231 
0.156 
015 
0.017 



52.764 



IV. 



0.005 
0.291 
0.321 
0.051 
0.053 
1.724 
51.754 



V. 



0.004 
0.067 
0.065 
0.045 
0.007 
1.168 
51.134 



VI. 



0.007 
0.169 
0.154 
0.042 
0.021 



50.765 



Properties of Wrought Irou. 

SrECiFic Gravity, 7.4 to 7.9. 

Weight per Cubic Foot, 480 to 487, usually taken at 480. 
Atomic Weight, 56. 
Melting-point. 2732° to 3000° F. 
Specific Heat, .1138. 

Conductivity of heat, 11.9, of electricity, 12 to 14.8 (silver 
being 100). 

Expansion by Heat in bulk between 32° aud 212° F. = .0035. 
Bars will expand or contract .000006614 of an inch, or the 
151,200lh part of their length, or about i iuch in 1562 feet for 
each degree of heat. Between the extremes —20° F. and +120° F. 



METALS. — WEOUGHT IRON. 



103 



a bar will expand, or contract .000926, or the lOSOtli part of its 
length a variation equivalent to a strain of 9^ tons per square 
inch o section For a variation in temperature of 125° a bar 
100 feet long will expand or contract 1.039 inches; with a varia- 
tion ot 15 the expauMou or contraction is about ' nt tho 
length, and the strain thus induced if the end' aLS r^iS, 
fixed will be about 1 ton per square Inch 

„pSTr'"°^-T^'''" ^ ''"'' "' ""-""^h' ""^ *« heated to red- 
bef o.i '^"'" '° '"''''' '' ^'''""^^' permanently shorter than 

Extension per pound of tensile force = .0000000357 of the 
ength or about 1 inch in 1000 feet, or i inch in 125 feet for every 
ton of tensile strain per square inch up to the elastic limit. 

Ultimate Stbength. 

^^'""^■•.- ••• 30,000 to 70,000pounds 

Compressive 40,ooo to 127,720 " 



SheariDg. 



40,000 



Working Strength. 

^^''^'^^' • ; 10,000 to 15,000 lbs. per sq. in 

Compressive 36,000- - - «' 

^^^^^'^^g 6000 to 9000" - '* *' 



Strength of Welds. 



strength of solid bar 
Strength of weld .... 



Tie-bars. 
Pounds. 



43,201 to 57,065 
17,816 to 44,586 



Plates. 
Pounds. 



44,851 to 47,481 
26,442 to 38,931 



Chains. 
Pounds. 



49,122 to 57,875 
39,575 to 48,824 



Welding heat is about 2733° F. ' 

Elongation ranges from 5 to 30 per cent of the original length 
^^Reductiok oe Akea at Pkactuke varies from^55 to 25^, 

Modulus of Elasticity. 22,000,000 to 29,000 000 

Tenacity at High Tempekatures. -The strength of wrouirht 

iron increases w th temperature from ft» „r, , "i wiouj,nt 

from 400° to fiOft°T? .. "r""^"'^\*^io'" "P to a maximum at 

irom 4U0 to 600 F„ the increase being from 8000 to 10,000 pounds 

6000 lbs. per square inch is shown at 1500° F. 



104 METALS.— WROUGHT IROK. 



Mill Inspection of Wrought Iron. 

In the mill iuspection of wrought iron no tests can be mad^ 
before the material is rolled. 

Witli the same kind of muck-bar and the same kiud of scrap, 
each pile will generally be found to differ from all the others; 
and because of this difference it is necessary, in order to ascertain 
its fitness for a specific purpose, to subject it to careful and 
accurate tests. The following are the usual requirements: 
It must be tough, ductile, and fibrous, free from cinder- 
pockets, flaws, buckles, blisters, and cracks along the edges. 

Toughness is indicated by a fine, close, and uniform fibrous 
structure, free from all appearance of crystallization, with a clear 
bluish-gray color and silky lustre on a torn surface where the 
fibres are exposed. 

Badly Refined Iron is indicated by coarse crystals, blotches 
of color, loose, open, and blackish fibres. Flaws in the fractured 
surface denote that the piling and welding processes were imper- 
fectly carried out. 

Good Iron is indicated by small crystals of a uniform size and 
color and fine, close, silky fibres. Good iron is readily heated, 
is soft under the hammer, and throws out few sparks. 

A soft, tough iron, if broken gradually gives long, silky fibres 
of leaden-gray hue, which twist together and cohere before 
breaking, broken rapidly the .fracture will have a crystalline 
appearance. 

Iron if brought to a white heat is injured if it be not at the 
same time hammered or rolled. 

Cold-short Iron. — Iron containing phosphorus is brittle 
wheu cold, and will crack if bent double. Cold-short iron is 
indicated by either a fine grain and steely appearance, or a coarse 
grain with bright crystalline fracture, and discolored spots. 

Red SHORT Iron.— Iron containing sulphur, copper, arsenic, 
and other impurities will crack when bent at a red heat, but has 
considerable tenacity when cold. It cannot be welded. Such 
iron is termed "red-short." Cracks on the edge of a bar are 
indications of red-short iron. 



METALS, — WROUGHT IRON. 105 



Tests for Wrought Iron. 

Bending Test (Cold). — Good iron should bend cold 180 
degrees around a curve whose diameter is twice the thickness of 
the piece for bar iron and three times the thickness for plates and 
shapes. 

Bending Test (Hot). — Iron which is to be worked hot must 
be capable of bending sharply to a right angle at a working heat 
without sign of fracture. 

Nicking and Bending. — Specimens upon being nicked on 
one side and bent should show a fracture nearly all fibrous. 

Rivet iron should be tough and soft, and be capable of bend- 
ing cold until the sides are in close contact without sign of frac- 
ture on the convex side of the curve. 

The tensile strength, limit of elasticity , and ductility are deter- 
mined from test-pieces cut from the full-sized bar. The number 
and size of the test-pieces will be governed by the specification. 
Test-pieces are usually cut about 18 inches long, 1 inch in width 
at the reduced portion, and of the same thickness as the piece 
from which it was taken. The area of cross-section ought not be 
less than half a square inch. 

Iron heated and suddenly cooled in water is hardened, and the 
breaking strain (if gradually applied) is increased, but it is more 
likely to snap suddenly. If heated and allowed to cool grad- 
ually, it is softened, and its breaking strain is reduced. 



106 



METALS. — WROUGHT IR0:N'. 



Table 12. 

WEIGHT OF FLAT BAR IRON PER LINEAL FOOT. 

At 480 lbs. per cubic foot. For steel add 1/48. 



5^ 

a; .- 


Thicknes 


S, IN 


Fractions of Inches. 






-h 


1 

8 


A 


L 
4 


5 
TB" 


i 


l^ 


i 


A 


f 


+4 




0.208 


0.417 


0.625 


0.833 


1.04 


1.25 


1.46 


1.67 


1.88 


2.08 


2.29 


Ig 


0.234 


0.469 


0.703 


0.938 


1.17 


1.41 


1.64 


1.87 


2.11 


2.34 


2.58 


n 


0.260 


0.521 


0.781 


1.040 


1.30 


1.56 


1.82 


2.08 


2.34 


2.60 


2.86 


n 


0.286 


0.573 


0.859 


1.150 


1.43 


1.72 


2.01 


2.29 


2.58 


2.86 


3.15 


H 


0.313 


0.625 


0.938 


1.250 


1.56 


1.88 


2.19 


2.50 


2.81 


3.13 


3.44 


16 


0.339 


0.677 


1.020 


1.360 


1.69 


2.03 


2.37 


2.71 


3.05 


3.39 


3.73 


Ig 


0.365 


0.729 


1.090 


1.460 


1.82 


2.19 


2.55 


2.92 


3.28 


3.65 


4.01 


1| 


0.391 


0.781 


1.170 


1.560 


1.95 


2.34 


2.73 


3.12 


3.51 


3.91 


4.30 


2 


0.417 


0.833 


1.250 


1.670 


2.08 


2.50 


2.92 


3.33 


3.75 


4.17 


4.58 


2| 


0.44:3 


0.886 


1.330 


1.770 


2.21 


2.65 


3.10 


3.54 


3.98 


4.43 


4.87 


2| 


0.469 


0.938 


1.410 


1.880 


2.34 


2.81 


3.28 


3.75 


4.22 


4.69 


5.16 


2i 


0.495 


0.990 


1.480 


1.980 


2.47 


2.97 


3.46 


3.96 


4.46 


4.95 


5.44 


25 


0.521 


1.040 


1.560 


2.080 


2.60 


3.13 


3.65 


4.17 


4.69 


6.21 


5.73 


2;' 


0.547 


1.090 


1.640 


2.190 


2.73 


3.28 


3.83 


4.38 


4.92 


5.47 


6.02 


2] 


0.573 


1.150 


1.720 


2.290 


2.86 


3.44 


4.01 


4.58 


5.16 


5.73 


6.30 


2| 


0.599 


1.200 


1.800 


2.400 


3.00 


3.60 


4.20 


4.79 


6.39 


6.99 


6.59 


3 


0.625 


1.250 


1.880 


2.500 


3.13 


3.75 


4.38 


5.00 


6.63 


6.25 


6.88 


34 


0.677 


1.350 


2.030 


2.710 


3.39 


4.06 


4.74 


5.42 


6.09 


6.77 


7.45 


35 


0.729 


1.460 


2190 


2.920 


3.65 


4.38 


5.10 


6.83 


6.56 


7.29 


8.02 


35 


0.781 


1.560 


2.340 


3.130 


3.91 


4.69 


5.47 


6.25 


7.03 


7.81 


8.59 


4 


0.833 


1.670 


2.500 


3.330 


4.17 


5.00 


5.83 


6.67 


7.50 


8.33 


9.17 


^4 


0.885 


1.770 


2.660 


3.540 


4.43 


5.31 


6.20 


7.08 


7.97 


8.85 


9.74 


45 


0.938 


1.880 


2.810 


3.750 


4.69 


5.63 


6.56 


7.50 


8.44 


9.38 


10.31 


4g 


0.990 


1.980 


2.970 


3.960 


4.95 


5.94 


6.93 


7.92 


8.91 


9.90 


10.89 


6 


1.042 


2.080 


3.130 


4.170 


5.21 


6.25 


7.29 


8.33 


9.38 


10.42 


11.46 


5| 


1.090 


2.190 


3.280 


4.380 


5.47 


6.56 


7.66 


8.75 


9.84 


10.94 


12.03 


1.150 


2.290 


3.440 


4.580 


5.73 


6.88 


8.02 


9.17 


10.31 


11.46 


12.60 


55 


1.200 


2.400 


3.590 


4.790 


5.99 


7.19 


8.39 


9.58 


10.78 


11.98 


13.18 


6 


1.250 


2.500 


3.750 


5.000 


6.25 


7.50 


8.75 


10.00 


11.25 


12.50 


13.75 


64 


1.300 


2.600 


3.910 


5.210 


6.51 


7.81 


9.11 


10.42 


11.72 


13.02 


14.32 


65 


1..350 


2.710 


4.060 


5.420 


6.77 


8.13 


9.48 


10.83 


12.19 


13.54 


14.90 


63 


1.410 


2.810 


4.220 


5.630 


7.03 


8.44 


9.84 


11.25 


12.66 


14.06 


15.47 


7 


1.460 


2.920 


4.380 


5.830 


7.29 


8.75 


10.21 


11.67 


13.13 


14.58 


16.04 


74 

75 


1.510 


3.020 


4.530 


6.040 


7.55 


9.06 


10.57 


12.08 


13.59 


15.10 


16.61 


1.560 


3.130 


4.690 


6.250 


7.81 


9.38 


10.94 


12.50 


14.06 


15.63 


17.19 


73 


1.610 


3.230 


4.840 


6.460 


8.07 


9.69 


11.30 


12.92 


14.53 


16.15 


17.76 


8 


1.670 


3..330 


5.000 


6.670 


8..33 


10.00 


11.67 


13.33 


15.00 


16.67 


18.33 


^1 


1.720 


3.440 


5.160 


6.880 


8.59 


10..31 


12.03 


13.75 


15.47 


17.19 


18.91 


1.770 


3.540 


5.310 


7.080 


8.85 


10.63 


12.40 


14.17 


15.94 


17.71 


19.48 


83 


1.820 


3.6.')0 


5.470 


7.290 


9.11 


10.94 


12.76 


14.58 


16.41 


18.23 


20.05 


9 


1.880 


3.750 


5.630 


7.500 


9.38 


11.25 


13.13 


15.00 


16.88 


18.75 


20.63 


91 
9i 


1.930 


3.850 


5.780 


7.710 


9.64 


11.56 


13.49 


15.42 


17.34 


19.27 


21.20 


1.980 


3.960 


5.940 


7.920 


9.90 


11.88 


13.85 


15.83 


17.81 


19.79 


21.77 


93 


2.030 


4.060 


6.090 


8.130 


10.16 


12.19 


14.22 


16.25 


18.28 


20.31 


22.34 


10 


2.080 


4.170 


6.250 


8.3.30 


10.42 


12..50 


14.58 


16.67 


18.75 


20.83 


22.92 


loi 
loi 


2.140 


4.270 


6.410 


8.540 


10.68 


12.81 


14.95 


17.08 


19.22 


21.35 


23.49 


2.190 


4.380 


6.560 


8.750 


10.94 


13.13 


15.31 


17.50 


19.69 


21.88 


24.06 


103 


2.240 


4.4H0 


6.720 


8.060 


11.20 


13.44 


15.68 


17.92 


20.16 


22.40 


24.64 


11 


2.290 


4.581 > 


6.HS0 


9.170 


11.46 


13.75 


16.04 


18.33 


20.63 


22.92 


25.21 


Hi 


2.340 


4.690 


7.030 


9.380 


11.72 


14.06 


16.41 


18.76 


21.09 


23.44 


25.78 


114 


2.400 


4.790 


7.190 


9.580 


11.98 


14.38 


16.77 


19.17 


21.56 


23.96 


26.35 


Hi 


2.450 


4.900 


7. .340 


9.790 


12.24 


14.69 


17.14 


19.58 


22.03 


24.48 


26.93 


12 


2.500 


5.0<J0 


7.500 


10.000 


12.50 


15.00 


17.50 


20.00 


22.50 


25.00 


27.50 



METALS. — WROUGHT IRON. 10? 

WEIGHT OF FLAT BAR IRON PER LINEAL FOOT. {Continued.) 



51 

ll 

pq a 


Thickness, in Fractions of Inches. I 

1 




+1 


I 


if 


1 


iiV 


H 


lA 


li 


lA 


li 




2.50 


2.71 


2.92 


3.13 


3.33 


3.54 


3.75 


3.96 


4.17 


4.37 


4.58 


la 


2.81 


3.05 


3.28 


3.52 


3.75 


3.98 


4.22 


4.45 


4.69 


4.92 


5.16 


I4 


3.13 


3.39 


3.65 


3.91 


4.17 


4.43 


4.69 


4.95 


5.21 


5.47 


5.73 


li 


3.44 


3.72 


4.01 


4.30 


4.58 


4.87 


5.16 


5.44 


5.73 


6.02 


6.30 


1^ 


3.75 


4.06 


4.38 


4.69 


5.00 


5.31 


5.63 


5.94 


6.25 


6.56 


6.88 


i| 


4.06 


4.40 


4.74 


5.08 


5.42 


5.75 


6.09 


6.43 


6.77 


7.11 


7.45 


12 


4.38 


4.74 


5.10 


5.47 


5.83 


6.20 


6.56 


6.93 


7.29 


7.66 


8.02 


i| 


4.69 


5.08 


5.47 


5.86 


6.25 


6.64 


7.03 


7.42 


7.81 


8.20 


8.59 


2 


5.00 


5.42 


5.83 


6.25 


6.67 


7.08 


7.50 


7.92 


8.33 


8.75 


9.17 


2| 


5.31 


5.75 


6.20 


6.64 


7.08 


7.52 


7.97 


8.41 


8.85 


9.30 


9.74 


1 


5.63 


6.09 


6.56 


7.03 


7.50 


7.97 


8.44 


8.91 


9.38 


9.84 


10.31 


5.94 


6.43 


6.93 


7.42 


7.92 


8.41 


8.91 


9.40 


9.90 


10.39 


10.89 


25 


6.25 


6.77 


7.29 


7.81 


8.33 


8.85 


9.38 


9.90 


10.42 


10.94 


11.46 


2 


6.56 


7.11 


7.66 


8.20 


8.75 


9.30 


9.84 


10.39 


10.94 


11.48 


12.03 


2| 


6.88 


7.45 


8.02 


8.59 


9.17 


9.74 


10.31 


10.89 


11.46 


12.03 


12.60 


2| 


7.19 


7.79 


8.39 


8.98 


9.58 


10.18 


10.78 


11.38 


11.98 


12.58 


13.18 


3 


7.50 


8.13 


8.75 


9.38 


10.00 


10.63 


11.25 


11.38 


12.50 


13.13 


13.75 


34 


8.13 


8.80 


9.48 


10.16 


10.83 


11.51 


12.19 


12.86 


13.54 


14.22 


14.90 


35 


8.75 


9.48 


10.21 


10.94 


11.67 


12.40 


13.13 


13.85 


14.58 


15.31 


16.04 


3| 


9.38 


10.16 


10.94 


11.72 


12.50 


13.28 


14.06 


14.84 


15.63 


16.41 


17.19 


4 


10.00 


10.83 


11.67 


12.50 


13.33 


14.17 


15.00 


15.83 


16.67 


17.50 


18.33 


4i 


10.63 


11.51 


12.40 


13.28 


14.17 


15.05 


15.94 


16.82 


17.71 


18.59 


19.43 


45 


11.25 


12.19 


13.13 


14.06 


15.00 


15.94 


16.88 


17.81 


18.75 


19.69 


20.63 


4| 


11.88 


12.86 


13.85 


14.84 


15.83 


16.82 


17.81 


18.80 


19.79 


20.78 


21.77 


5 


12.50 


13.54 


14.58 


15.63 


16.67 


17.71 


18.75 


19.79 


20.83 


21.88 


22.C2 


^\ 


13.13 


14.22 


15.31 


16.41 


17.50 


18.59 


19.69 


20.78 


21.88 


22.97 


24.0S 


6i 


13.75 


14.90 


16.04 


17.19 


18.33 


19.48 


20.63 


21.77 


22.92 


24.08 


25.21 


5| 


14.38 


15.57 


16.77 


17.97 


19.17 


20.36 


21.56 


22.76 


23.96 


25.16 


26.r.5 


6 


15.00 


16.25 


17.50 


18.75 


20.00 


21.25 


22.50 


23.75 


25.00 


26.25 


27.no 


64 
65 


15.63 


16.93 


18.23 


19.53 


20.83 


22.14 


23.44 


24.74 


26.04 


27.34 


28.65 


16.25 


17.60 


18.96 


20.31 


21.67 


23.02 


24.38 


25.73 


27.08 


28.44 


29.79 


64 


16.88 


18.28 


19.69 


21.09 


22.50 


23.91 


25.31 


26.72 


28.13 


29.53 


30.94 


7 


17.50 


18.96 


20.42 


21.88 


23.33 


24.79 


26.25 


27.71 


29.17 


30.62 


32.08 


7| 


18.13 


19.64 


21.15 


22.66 


24.17 


25.68 


27.19 


28.70 


30.21 


31.72 


33.23 


71 


18.75 


20.31 


21.88 


23.44 


25.00 


26.56 


28.13 


29.69 


31.25 


32.81 


34.38 


n 


19.38 


20.99 


22.60 


24.22 


25.83 


27.45 


29.06 


30.68 


32.29 


33.91 


35.52 


8 


20.00 


21.67 


23.33 


25.00 


26.67 


28.33 


30.00 


31.67 


33.33 


35.00 


36.67 


84 


20.63 


22.34 


24.06 


25.78 


27.50 


29.22 


30.94 


32.66 


34.38 


36.09 


37.81 


85 


21.25 


23.02 


24.79 


26.56 


28.33 


30.10 


31.88 


33.65 


35.42 


37.19 


38.96 


8| 


21.88 


23.70 


25.52 


27.34 


29.17 


30.99 


32.81 


34.64 


36.46 


38.28 


40.10 


9 


22.50 


24.38 


26.25 


28.13 


30.00 


31.88 


33.75 


35.63 


37.50 


39.38 


41.25 


9^ 


23.13 


25.05 


26.98 


28.91 


30.83 


32.76 


34.69 


36.61 


38.54 


40.47 


42.40 


4 


23.75 


25.73 


27.71 


29.69 


.31.67 


33.65 


35.63 


37.60 


39.58 


41.56 


43.54 


9| 


24.38 


26.41 


28.44 


30.47 


32.50 


34.53 


36.56 


38.59 


40.63 


42.66 


44.69 


10 


25.00 


27.08 


29.17 


31.25 


33.33 


35.42 


37.50 


39.58 


41.67 


43.75 


45.83 


10^ 


25.62 


27.76 


29.90 


32.03 


34.17 


36.30 


38.44 


40.57 


42.71 


44.84 


46.98 


10^ 


26.25 


28.44 


30.63 


32.81 


35.00 


37.19 


39.38 


41.56 


43.75 


45.94 


48.13 


log 


26.88 


29.11 


31 .35 


33.59 


35.83 


38.07 


40.31 


42.55 


44.79 


47.03 


49.27 


11 


27.50 


29.79 


32.08 


34.38 


36.67 


38.96 


41 .25 


43.54 


45.83 


48.13 


50.42 


m 


28.13 


30.47 


32.81 


35.16 


37.50 


39.84 


42.19 


44.53 


46.88 


49.22 


51.56 


i\\ 


28.75 


31.15 


33.54 


35.94 


38.33 


40.73 


43.13 


45.52 


47.92 


50.31 


52.71 


115 


29.38 


31.82 


34.27 


36.72 


39.17 


41 .61 


44.06 


46.51 


48.96 


51.41 


53.85 


12 


30.00 


32.50 


35.00 


37.50 


40.00 


42.50 


45.00 


47.50 


50.00 


52.50 


55.00 



108 



METALS.— WROUGHT IROK AND STEEL. 



Table 13. 

WROUGHT IRON AND STEEL.— WEIGHT OF PLATES, ROUND 
AND SQUARE BARS. 



Thickness or 




Wt. 


Wt. of 




Thickness 


Wt 


Wt. of 


Wt. of 




Diani. 


Wt. of 

a 
Sq. Ft. 


of a 
Square 
Bar 1ft. 


a 
Round 
Bar 1 ft. 


Wt. of 
Balls. 


or Diam. 


of a 
11 


aSq. 
Bar 
1ft. 


a 

Round 

Bar 

1 ft. 


Wt. of - 
BaUs. 




Dec. 




Dec. 


In. 


of a 




long. 


long. 




In. 


of a 




long. 


long. 






Foot. 


Lbs. 


Lbs. 


Lbs. 


Lbs. 




Foot. 


Lbs. 


Lbs. 


Lbs. 


Lbs. 


1/3-^ 


.0026 


1.263 


.0033 


.0026 




3^^ 


.2604 


126.3 


32.86 


25.83 


4.484 


1/16 


.0052 


2.526 


.0132 


.0104 




^ 


2708 


131.4 


35.57 


27.94 


5.045 


3/3-2 


.0078 


3.789 


.0296 


.0233 


.0001 


% 


.2813 


136.4 


38.37 


30.13 


5.649 


H 


.0104 


5.052 


.0526 


.0414 


.0003 


y<i 


.2917 


141.5 


41.26 


32.41 


6.301 


5/32 


.0130 


6.315 


.0823 


.0646 


.0005 


% 


.3021 


146.5 


44.26 


34.76 


7.000 


3/16!. 0156 


7.578 


.1184 


.0930 


.0009 


% 


.3125 


151.6 


47.37 


37.20 


7.750 


7/32 


.0132 


8.841 


.1612 


.1266 


.0015 


Vs 


.3229 


156.6 


50.57 


39.72 


8.550 


M 


.0208 


10.10 


.2105 


.1653 


.0023 


4 


.3333 


161.7 


53.89 


42.33 


9.405 


9/32 


.0234 


11.37 i .2665 


.2093 


.0033 


v^ 


.3438 


166.7 


57.31 


45.01 


10.32 


5/ 16!. 0260 


12.63 


.3290 


.2583 


.0045 


M 


.3542 


171.8 


60.84 


47.78 


11.28 


11/321.0287 


13.89 


.3980 


.3126 


.0060 




.3646 


176.8 


64.47 


50.63 


12.31 


% .0313 


15.16 


.4736 


.3720 


.0078 


Ty^ 


.3750 


181.9 


68.20 


53.57 


13.39 


13/32 .0339 


16.42 


.5558 


.4365 


.0098 


5^ .3854 


186.9 


72.05 


56.59 


14.54 


7/161.0365 


17.68 


.6446 


.5063 


.0123 


^ 


.3958 


192.0 


76.99 


59.69 


15.75 


15/32 


.0391 


18.95 


.7^00 


.5813 


.0151 


% 


.4063 


197.0 


80.05 


62.87 


17.03 


Vu 


.0417 


20.21 


.8420 


.6613 


.0184 


5 


.4167 


202.1 


84.20 


66.13 


18.37 


9/16 


.0469 


22.73 


1.066 


,8370 


.0262 


% 


.4271 


207.1 


88.47 


69.48 


19.78 


% 


.0521 


25.26 


1.316 


1.033 


.0359 


Va 


.4375 


212.2 


92.83 


72.91 


21.26 


11/16 


.0573 


27.79 


1.592 


1.250 


.0478 


% 


.4479 


217.2 


97.31 


76.43 


22.82 


3^ 


.0625 


30.31 


1.895 


1.488 


.0620 




.4583 


222.3 


101.9 


80.02 


24 45 


13/16 


.0677 


32.84 


2,223 


1.746 


.0788 


v% 


.4688 


227.3 


1C6.6 


83.70 


26.16 


% 


.0729 


35.87 


2.579 


2.025 


.0985 


H 


.4792 


232.4 


111.4 


87.46 


27.94 


15/16'. 0781 


37.89 


2.960 


2.325 


.1211 


Vs 


.4896 


237.5 


116.3 


91.31 


29.80 


1 


.0833 


40.42 


3.368 


2.645 


.1470 


6 


.5000 


242.5 


121.3 


95.23 


31.74 


1/16 


.0885 


42.94 


3.803 


2.986 


.1763 




.5208 


252.6 


131.6 


103.3 


35.88 


H 


.0938 


45.47 


4.263 


3.348 


.2093 


L^ 


.5417 


262.7 


142.3 


111.8 


40.36 


3/16 


.0990 


48.00 


4.750 


3.730 


.2461 


% 


.5625 


272.8 


153.5 


120.5 


45.19 


H 


.1042 


50.52 


5.263 


4.133 


.2870 




,5833 


282.9 


165.0 


129.6 


50.40 


5/16 


.1094; 53.05 


5.802 


4.557 


.3323 


M 


.6042 


293.0 


177.0 


139.0 


56.00 


% 


.1146, 55.57 


6.368 


5.001 


.3-20 




.6250 


303.1 


189.5 


148.8 


62.00 


7/16 .1198' 58.10 


6.960 


5.466 


.4365 


% 


.6458 


313.2 


202.3 


158.9 


68.40 


% 1.1250, 60.63 


7.578 


5.952 


.4960 


8 


.6667 


323.3 


215.6 


169.3 


75.24 


9/16.130? 63.15 


8.223 


6.458 


.5606 


1/ 


.6875 


333.4 


229.3 


180.1 


82.52 


% .1354 


65.68 


8.893 


6.985 


.6306 


\^ 


.7083 


:343.5 


243.4 


191.1 


90.25 


11/16 .1406 


68.20 


9.591 


7.533 


.7062 


% 


.7292 


353.6 


247.9 


202.5 


98.45 


% .1458 


70.73 


10.31 


8.101 


.7876 


9 


.7500 


363.8 


272.8 


214.3 


107.1 


13/16 


.1510 


73.26 


11.07 


8.690 


.8750 


M 


.7708 


373.9 


288.2 


226.3 


116.3 


H 


.1563 


75.78 


11.81 


9.300 


.9688 




.7917 


384.0 


304.0 


238.7 


126.0 


15/16 


.1615 


78.31 


12.64 


9.930 


1.069 


% 


.8125 


394.1 


320.2 


251.5 1 


136.2 


2 


.1667 


80.83 


13.47 


10.58 


1.176 


10 


.8333 


404.2 


336.8 


264.5 


146.9 


H 


.1771 


85.89 


15.21 


11.95 


1.410 


Va 


.8542 


414.3 


353.9 


277.9 


158.2 


H 


.1875 


90.94 


17.05 


13.39 


1.674 




.8750 


424.4 


371.3 


291.6 


170.1 


.1979 95.99 


19.00 


14.92 


1.969 


% 


.8958 


434.5 


389.2 


305.7 


182.6 


^ 


.2083 101.0 


21.05 


16.53 


2.296 


11 


.9167 


444.6 


407.5 


320.1 


195.6 


% 


.2188 106.1 


23.21 


18.23 


2.658 


\A 


.9375 


454.7 


426.3 


334.8 1 


209.2 


^ 


.2292 111.2 


25.47 


20.01 


3.056 


ik 


.9583 


464.8 


445.4 


349.8 I 


223.5 


% 


.2396 116.2 


27.84 


21.87 


3.492 


Va 


.9792 


474.9 


465.0 


365.2 ' 


238.4 


3 


.2500 121.3 


30.31 


23.81 


3.968 J 


12 1 1 f t ' 


485.0 


485.0 


380.9 


253.9 



Wrouj^ht iron is here taken at 485 lbs. per cu. ft. Very pure soft wrought 
iron weip^hs f lom 488 to 492 lbs. per cu. ft. Light weight indicates impurities 
and weakness. Steel weighs about 490 lbs. per cu. ft.; therefore for stekl 

AN ADDITION MUST BE MADE TO THE TABULAR AMOUNTS OF ABOUT 1 LB. IN 
100 LBS. 

At 485 lbs. percu. ft. a cubic inch weighs .280671b.; a lb. contains 3.5629 
cMi. in., and a ton, 4.G186 cu. ft.; and this is about the average of hammered 
iron. The usual assumption is 480 lbs. per cu. ft., which is nearer the aver- 
age of ordinary rolled iron. At 480 lbs. a cubic inch weighs .2778 of a lb.; a 
lb. contains 3.6 cu. in.; a ton 4.6067 cu. ft.; a rod of 1 sq. in. area weighs 10 
lbs. per yard, or S}^ lbs. per foot, exactly. 



METALS.— STEEL. 



•08rt 



Table ISa, 

WEIGHTS OF ROUND AND SQUARE STEEL PER LINEAL FOOT. 

One cubic foot of steel weighs 490 lbs. 



Sizes 


o 


a 


Sizes 


O 


D 


iSizes 


o 


D 


in 


Weight 


Weight 


in 


Weij>ht 


Weight 


in 


Weight 


Weight 


Inches. 


in Lbs. 


in Lbs 


Inches. 


in Lbs. 
44.07 


in Lbs. 


Inches. 


in Ll)s. 


ill Lbs. 


1/1« 


.010 


.013 


4 1/16 


56.11 


8 1/16 


173.6 


TZl.O 


Va 


.042 


.053 


Vs 


45.44 


57.85 


Vs 


176.3 


224.5 


3/16 


.094 


.119 


3/1 G 


4G.83 


59.62 


3/16 , 


179.0 


228.0 


M 


.167 


.212 


H 


48.24 


61.41 


■4 


181.8 


231.4 


5/16 


.261 


.333 


5/16 


49.66 


63.23 


5/16 


184.5 


234.9 


% 


.375 


.478 


% 


51.11 


65.08 


% 


187.3 


238.5 


7/16 


.511 


.651 


7/16 


52.. 58 


66.95 


7/16 


190.1 


242.0 


^ 


.667 


.850 


V2 


54.07 


68.85 


Vq 


193.0 


245.6 


9/16 


.845 


1.076 


9/16 


55.59 


70.78 


9/16 


195.7 


249.3 


% 


1.043 


1.328 


% 


57.12 


72.73 


% 


198.7 


252.9 


11/16 


1.262 


1.608 


11/16 


58.67 


74.70 


11/16 


201.6 


256 6 


M 


1.502 


1.913 


H 


60.25 


76.71 


% 


204.4 


260.3 


13/16 


1.763 


2.245 


13/16 


61.84 


78.74 


13/16 


207.4 


264.1 


Vs 


2.044 


2.603 


% 


63.46 


80.81 


% 


210.3 


267.9 


15/16 


2.347 


2 989 


15/16 


65.10 


82.89 


15/16 


213.3 


271.6 


1 


2.670 


3.400 


5 


66.76 


85.00 


9 


216.3 


275.4 


1/16 


3.014 


3.838 


1/16 


68.44 


87.14 


1/16 


219.3 


279.3 


H 


3.379 


4.303 


% 


70.14 


89.30 


% 


222.4 


283.2 


3/16 


3.766 


4.795 


3/16 


71.86 


91.49 


3/16 


225.4 


287.0 


H 


4.173 


5.312 


H 


73.60 


93.72 


H 


228.5 


290.9 


5/16 


4.600 


5.857 


5/16 


75.37 


95.96 


5/16 


231.5 


294.9 


% 


5.049 


6.428 


% 


77.15 


98.23 


V8 


234.7 


298.9 


7/16 


5.518 


7.026 


7/16 


78.95 


100.5 


7/16 


237.9 


302.8 


^2 


6.008 


7.650 


V2 


80.77 


102.8 


y2 


241 


306.8 


9/16 


6.520 


8.301 


9/16 


82.62 


105.2 


9/16 


244.2 


310 9 


% 


7.051 


8.978 


% 


84.49 


107.6 


% 


247.4 


315 


11/16 


7.604 


9.6^2 


11/16 


86.38 


110.0 


11/16 


250.6 


319.1 


% 


8.178 


10.41 


H 


88.29 


112.4 


M 


253.9 


323.2 


13/16 


8.773 


11.17 


13/16 


90.22 


114.9 


13/16 


257.1 


327.4 


% 


9.388 


11.95 


% 


92.17 


117.4 


Va 


260.4 


331.6 


15/16 


10.02 


12.76 


15/16 


94.14 


119.9 


15/16 


263.7 


335.8 


2 


10.68 


13.60 


6 


96.14 


122.4 


10 


267.0 


340.0 


1/16 


11.36 


14.46 


1/16 


98.14 


125.0 


1/16 


270.4 


344.3 


y8 


12.06 


15.35 


Vs 


100.2 


127.6 


Vs 


273.7 


348.5 


3/16 


12.78 


16.27 


3/16 


102.2 


130.2 


3/16 


277.1 


352.9 


M 


13.52 


17.22 


M 


104.3 


132.8 


H 


280.6 


357.2 


5/16 


14.28 


18.19 


5/16 


106.4 


135.5 


5/16 


284.0 


361.6 


% 


15.07 


19.18 


% 


108.5 


138.2 


"A 


287.4 


366.0 


7/16 


15.86 


20.20 


7/16 


110.7 


140.9 


7/16 


290.9 


370.4 


^ 


16.69 


21.25 


% 


112.8 


143.6 


K 


294.4 


374 9 


9/16 


17.53 


22.33 


9/16 


114.9 


146.5 


9/16 


297.9 


379.4 


Vs 


18.40 


23.43 


% 


117.2 


149.2 


Vs 


301.4 


383.8 


11/16 


19.29 


24.56 


11/16 


119.4 


152.1 


11/16 


305.0 


388.3 


M 


20.20 


25.00 


% 


121.7 


154.9 


H 


308.6 


392.9 


18/16 


21.12 


26.90 


13/16 


123.9 


157.8 


13/16 


312.2 


397.5 


% 


22.07 


28.10 


Vs 


126.2 


160.8 


% 


315.8 


402.1 


15/16 


23.04 


29.34 


15/16 


128.5 


163.6 


15/16 


319 5 


406.8 


3 


24.03 


30.60 


7 


130.9 


166.6 


11 


323.1 


411.4 


1/16 


25.04 


31.89 


1/16 


133.2 


169.6 


1/16 


326.8 


416.1 


H 


26.08 


33.20 


% 


135.6 


172.6 


H 


330.5 


420.9 


3/16 


27.13 


34.55 


3/16 


137.9 


175.6 


3/16 


334.3 


425.5 


^ 


28.20 


35.92 


M 


140.4 


178.7 


H 


337.9 


430.3 


5/lG 


29 30 


37.31 


5/16 


142.8 


181.8 


5/16 


341.7 


435.1 


3/6 


30.42 


38.73 


% 


145.3 


184.9 


% 


345.5 


439.9 


7/16 


31.56 


40.18 


7/16 


147.7 


188.1 


7/16 


349.4 


444.8 


^ 


32.71 


41.65 


^ 


150.2 


191.3 


H 


353.1 


449.6 


9/lG 


33.90 


43.14 


9/16 


152.7 


194.4 


9/16 


357.0 


454.5 


^ 


35.09 


44.68 


% 


155.2 


197.7 


% 


360.9 


459.5 


11/16 


36.31 


46.24 


11/16 


157.8 


200.9 


11/16 


3r.4.8 


464.4 


% 


37.56 


47.82 


% 


160.3 


204.2 


H 


868. 6 


469.4 


13/16 


38.81 


41). 42 


13/16 


163.0 


207.6 


13/16 


372.6 


474.4 


. % 


40.10 


51.05 


% 


165.6 


210.8 


% 


876.6 


479.5 


J5/1G 


41.40 


52.71 


15/1 r, 


168.2 


214.2 


15/16 


380.6 


484.5 


4 


42.73 


54.40 


8 


171.0 


217.6 









lOSb 



METALS. — STEEL. 



f 




















Table 


WEIGHTS OF FLAT ROLLED STEEL BARS PFR LINEAL 


Thick- 
ness 
in Ins. 


Width 


1" 


• i' 


w 


\\" 


T' 


1\" 


1\" 


2r' 


. 687 


Zk" 


3i"" 


1/16 


.2T2 


".265 


.319 


.372 


.425 


.478 


.531 


.584 


.690 


.743 


A 


.425 


.531 


.637 


.743' .8491 


.956 


1.06 


1.17 


1.28 


1.38 


1.49 


^16 


.688 


.797 


.957 


1.11 


1.28 


1.44 


1.59 


1.75 


1.91 


2.07 


2.23 


Va 


.850 


1.06 


1.28 


1.49 


1.70 


1.91 


2.12 


2.34 


2.55 


2.76 


2.98 


5/16 


1.00 


1.33 


1.59 


1.S6 


2.12 


2.39 


2.65 


2.92 


3.19 


3.45 


3.72 


% 


l.-JS 


1.59 


1.92 


2.23 


2.55 


2.87 


3.19 


3.51 


3.83 


4.15 


4.47 


7/16 


1.49 


1.86 


2.23 


2.60 


2.98 


3.35 


3.72 


4.09 


4.46 


4.83 


5.20 


]4 


1.70 


2.12 


2.55 


2.98 


3.40 


3.83 


4.25 


4.67 


5.10 


5.53 


5.95 


9/16 


1.92 


2.39 


2.87 


3.35 


3.83 


4.30 


4.78 


5.26 


5.74 


6.22 


6.70 


% 


2.12 


2.65 


3.19 


3.72 


4.25 


4.78 


5.31 


5.84 


6.38 


6.91 


7.44 


11/16 


2.84 


2.92 


3.51 


4.09 


4.67 


5.26 


5.84 


6.43 


7.02 


7.60 


8.18 


% 


2.55 


8.19 


3.88 


4.47 


5.10 


5.75 


6.38 


7.02 


7.65 


8.29 


8.93 


13/16 


2.76 


3.45 


4.14 


4.84 


5.53 


6.21 


6.90 


7.60 


8.29 


8.98 


9.67 


% 


2.98 


3.72 


4.47 


5.20 


5.95 


6.69 


7.44 


8.18 


8.93 


9.67 


10.41 


15/16 


3.19 


3.L9 


4.78 


5.58 


6.38 


7.18 


7.97 


8.77 


9.57 


10.36 


11.16 


1 


3.^0 


4.25 


5.10 


5.95 


6.80 


7.65 


8.50 


9.35 


10 20 


11.05 


11.90 


1/16 


3.61 


4.52 


5.42 


6.32 


7 22 


8.13 


9.03 


9.93 


10.84 


11.74 


12.65 


"k 


3.83 


4.78 


5.74 


6.70 


7^65 


8.61 


9.57 


10.52 


11.48 


12.43 


13.39 


3/16 


4.04 


5.05 


6.06 


7.07 


8.08 


9.09 


10.10 


11.11 


12.12 


13.12 


14.13 


M 


4.,'55 


5.31 


6.38 


7.44 


8.50 


9.57 


10.63 


11.69 


12.75 


13.81 


14.87 


5/16 


4.43 


5.58 


6.69 


7.81 


8.93 


10.04 


11.16 


12.27 


13.39 


14.50 


15.62 


% 


4.67 


5.84 


7.02 


8.18 


9.35 


10.52 


11.69 


12.85 


14.03 


15.20 


16.36 


7/16 


4.89 


0.11 


7.34 


8.56 


9.78 


11.00 


12.22 


13.44 


14.66 


15.88 


17.10 


^ 


5.10 


6.3S 


7.65 


8.98 


10.20 


11.48 


12.75 


14.03 


15.30 


16.58 


17.85 


9/lC 


5.82 


6.64 


7.97 


9.80 


10.63 


11.95 


13.28 


14.61 


15.94 


17.27 


18.60 


% 


5.52 


6.90 


8.29 


9.67 


11.05 


12.43 


13.81 


15.19 


16.58 


17.96 


19.34 


11/16 


5.74 


7.17 


8.61 


10.04 


11.47 


12.91 


14.34 


15.78 


17.22 


18.65 


20.08 


% 


5.95 


7.44 


8.93 


10.42 


11.90 


13.40 


14.88 


16.37 


17.85 


19.34 


20.83 


13/16 


6.16 


7.70 


9.24 


10.79 


12.33 


13.86 


15.40 


16.95 


18.49 


20.03 


21.57 


% 


6.38 


7.97 


9.57 


11.15 


12.75 


14.34 


15.94 


17.53 


19.13 


20.72 


22.31 


15/16 


6.59 


8.24 


9.88 


11.53 


13.18 


14.83 


16.47 


18.12 


19.77 


21.41 


23.06 


2 


6.80 


8.50 


10.20 


11.90 


13.60 


15.30 


17.00 


18.70 


20.40 


22.10 


23.80 




-7//- 


1\'^ 


Tt" 


1\>' 


8'' 


81- 


^\" 


"8^" 


9'^ 


1.97 


9i" 


1/16 


1.49 


1.54 


1.59 


1.65 


1.70 


1.75 


1.81 


1.86 


1.92 


2.02' 


% 


2.18 


3.08 


3.18 


3.29 


3.40 


3.50 


3.62 


3.72 


3.83 


3.92 


4.04 


3/16 


4.46 


4.62 


4.78 


4.94 


5.10 


5.26 


5.42 


5.58 


5.74 


5.90 


6.06 


^ 


5.95 


6.16 


6.36 


6.58 


6.80 


7.01 


7 22 


7.43 


7.65 


7.86 


8.08 


5/16 


7.44 


7.70 


7.97 


8.23 


8.50 


8.76 


903 


9.29 


9.56 


9.83 


10.10 


% 


8.93 


9.25 


9.57 


9.88 


10.20 


10.52 


10.84 


11.16 


11.48 


11.80 


12.12 


7/16 


10.41 


10.78 


11.16 


11.53 


11.90 


12.27 


12.64 


18.02 


13.40 


13.76 


14.14 


^ 


11.90 


12.82 


12.75 


13.18 


13.60 


14.03 


14.44 


14.87 


15.30 


15.73 


16.16 


9/16 


13.39 


18.86 


14.34 


14.82 


15.30 


15.78 


16.26 


16.74 


17.22 


17.69 


18.18 


% 


14.87 


15.40 


15.04 


16.47 


17.00 


17.53 


18.06 


18.59 


19.13 


19.65 


20.19 


11/16 


16.36 


16.94 


17.53 


18.12 


18.70 


19.28 


19.86 


20.45 


21.04 


21.62 


22.21 


¥a 


17.85 


18.49 


19.13 


19.77 


20.40 


21.04 


21.68 


22.32 


22.96 


23.59 


24.23 


13/16 


19.34 


20.03 


20.72 


21.41 


22.10 


22. ig 


23.48 


24.17 


24.86 


25.55 


26.24 


% 


20.83 


21.57 


22.82 


23.05 


28.80 


24.55 


25.30 


26.04 


26.78 


27.52 


28.26 


15/16 


22 32 


28.11 


23.91 


24.70 


25.50 


26.30 


27.10 


27.89 


28.69 


29.49 


30.28 


1 


23! 80 


24.65 


25.50 


26.85 


27.20 


28.05 


28.90 


29.75 


30.60 


81.45 


32.30 


1/16 


25.29 


26.19 


27.10 


28.00 


28.90 


29.80 


30.70 


31.61 


32.52 


38.41 


34.32 


\k 


26.78 


27.73 


28.68 


29.64 


30.60 


81.56 


32.52 


38.47 


34.43 


35.88 


86.34 


3/16 


28.26 


29.27 


30.28 


31.29 


32.80 


38.81 


84.32 


85.33 


86.34 


37.35 


38.36 


M 


29.75 


30.81 


81 . 88 


82.94 


34.00 


35.06 


86.12 


37.20 


38.26 


39.31 


40.87 


5/16 


31.23 


32.35 


33.48 


84.59 


35.70 


86.81 


87.98 


39 05 


40.16 


41.28 


42.40 


% 


32 72 


38.89 


35.06 


36.23 


37.40 


88.57 


89.74 


40.91 


42.08 


43.25 


44.41 


7/16 


34.21 


35.44 


36.66 


37.88 


39.10 


40.32 


41.51 


42.77 


44.00 


45.22 


46.44 


^ 


:i5.70 


36.98 


38.26 


39.53 


40.80 


42.08 


48.35 


44.68 


45.90 


47.18 


48.45 


9/16 


37.19 


3S.51 


89.84 


41.17 


42.50 


18.88 


45.16 


46.49 


47.82 


49.14 


50.48 


!^ 


3H.C7 


40.05 


41.44 


12.82 


44.20 


45.58 


S6.96 


48.34 


49.73 


51.10 


52.49 


11/16 


40.16 


41.59 


43.03 


44.47 


45.90 


47.83 


48.76 


50.20 


51.64 


53.07 


54.51 


Va 


141.65 


43.14 


44.68 


46.12 


47.00 


49,09 


50.58 


52.07 


53.56 


55.04 


56.53 


13/16 


43 U 


144.68 


'46.22 


47.76 


49.80 


50.84 


52. 3S 


53.92 


55.46 


57.00 


58.54 


'% 


44.63 


46.22 


47.82 


49.40 


51.00 


52 ()0 


51.20 


55.79 


57.88 


58.97 


60.56 


15/l(j 


46.12 


47.76 


49.41 


51.05 


52 70 


54 85 


56.00 


57.64 


159.29 


60.94 


62.58 


% 


47.r.() 


49.80 51.00 


52.70 


54.40 


.")»•. . 1 


r>7.so '59 .*>o 


if.i •'(> 


n».90 


i^'4.6> 



METALS. — STEEL. 



108c 



136. 

FOOT IN POUNDS. (One cubic foot of steel weighs 489.6 lbs.) 

of Bars. 'f 



3f" 


4" 


4i" 


4f-' 


M" 


5^' 


sr' 


^\" 


^l" 


6'' 

1.28 


1.33 


1.38 


er' 


797 


.849 


.902 


.956 


1.01 


1.06 


1.11 


1.17 


1.22 


1.43 


1.59 


1.70 


1.81 


i.92 


2.02 


2.12 


2.23 


2.34 


2.45 


2.55 


2.65 


2.76 


2.83 


2.39 


2.55 


2.71 


2.87 


3.03 


3.19 


3.35 


3.51 


3.67 


3.83 


3.99 


4.14 


4.30 


3.19 


3.40 


3.61 


3.83 


4.04 


4.25 


4.46 


4.67 


4.89 


5.10 


5.31 


5.53 


5.74 


3.99 


4.25 


4.52 


4.78 


5.05 


5.31 


5.58 


5.84 


6.11 


6.38 


6.64 


6.90 


7.17 


4.78 


5.10 


5.42 


5.74 


6.06 


6.38 


6.69 


7.02 


7.34 


7.65 


7.97 


8.29 


8.61 


5.58 


5.95 


6.32 


6.70 


7.07 


7.44 


7.81 


8.18 


8.56 


8.93 


9.29 


9.67 


10.04 


6.38 


6.80 


7.22 


7.65 


8.08 


8.50 


8.93 


9.35 


9.77 


10.20 


10.63 


11.05 


11.48 


7.17 


7.65 


8 13 


8.61 


9.09 


9.57 


10.04 


10.52 


11.00 


11.48 


11.95 


12.43 


12.91 


7.97 


8.50 


9 03 


9.57 


10.10 


10.03 


11.16 


11.69 


12.22 


12.75 


13.28 


13.81 


14.34 


8.76 


9.35 


9.93 


10.52 


11.11 


11.69 


12.27 


12.85 


13.44 


14.03 


14.61 


15.20 


15.78 


9 57 


10.20 


10.84 


11.48 


12.12 


12.75 


13.39 


14.03 


14.67 


15.30 


15.94 


16.58 


17.22 


10.36 


11.05 


11. r4 


12.43 


13.12 


13.81 


14.50 


15.19 


15.88 


16.58 


17.27 


17.95 


18.65 


11.16 


11.90 


12.65 


13.39 


14.13 


14.87 


15.62 


16.36 


17.10 


17.85 


18.60 


19.34 


20.08 


11 95 


12.75 


13.55 


14.34 


15.14 


15.94 


16.74 


17.53 


18.33 


19.13 


19.92 


20.72 


.21.51 


12. rs 


13.60 


14.45 


15.30 


16.15 


17.00 


17.85 


18.70 


19.55 


20.40 


21.25 


22.10 


22.95 


13.55 


14.45 


15.35 


16.26 


17.16 


18.06 


18.96 


19.87 


20.77 


21.68 


22.58 


23.48 


24.39 


14.34 


15.30 


16.26 


17.22 


18.17 


19.13 


20.08 


21.04 


21.99 


22.95 


23.91 


24.87 


25.82 


15.14 


16.15 


17.16 


18.17 


19.18 


20.19 


21.20 


22.21 


23.22 


24.23 


25.23 


26.24 


27.25 


15.94 


17.00 


18.06 


19.13 


20.19 


21.25 


22.32 


23.38 


24.44 


25.50 


26.56 


27.62 


28.69 


16.74 


17.85 


18.96 


20.08 


21.20 


22.32 


23.43 


24.54 


25.66 


26.78 


27.90 


29.01 


30.12 


17.53 


18.70 


19.87 


21.04 


22.21 


23.38 


24.54 


25.71 


26.88 


28.05 


29.22 


30.39 


31.56 


18.33 


19.55 


20.77 


21.99 


23.22 


24.44 


25.66 


26.88 


28.10 


29.33 


30.55 


31.77 


32.99 


19.13 


20.40 


21.68 


22.95 


24.23 


25.50 


26.78 


28.05 


29.33 


30.60 


31.88 


33.15 


34.43 


19.92 


21.25 


22.58 


23.91 


25.24 


26.57 


27.89 


29.22 


30.55 


31.88 


33.20 


34.53 


35.86 


20.72 


22.10 


23.48 


24.87 


26.25 


27.63 


29.01 


30.39 


31.77 


33.15 


34.53 


35.91 


37.29 


21.51 


22.95 


24.38 


>.'5.82 


27.26 


28.69 


30.12 


31.55 


32.99 


34.43 


35.86 


37.30 


38.73 


22.32 


23.80 


25.29 


26.78 


23.27 


29.75 


31.24 


32.73 


34.22 


35.70 


37.19 


38.68 


40.17 


23.11 


24.65 


26.19 


27.73 


29.27 


30.81 


32.35 


33.89 


35.43 


36.98 


38.52 


40.05i41.60 


23.91 


25.50 


27.10 


28.69 


3 J. 28 


31.87 


33.47 


35.06 


36.65 


38.25 


39.85 


41.44 


43.03 


24.70 


26.35 


28.00 


29.64 


31.29 


32.94 


34.59|36.23 


37.88 


39.53 


41.17 


42.82 


44.46 


25.50 


27.20 


28.90 


30.60 


32.30 


34.00 


35.70!37.40 


39.10 


40.80 


42.50 


44.20 


45.90 



9f' 10" lOi'' 10^'' 



2.12 
4.25 
6.38 
8.50 
10.62 
12.75 
14.88 
17.00 
19.14 
21.25 
23.38 
25.50 
27.62 
29.75 
31.88 
34.00 
36.12 
38.25 
40.38 
42.50 
44.64 
46.75 
48.88 
51.00 
53.14 
55.25 
57.39 
159.50 
61.62 
63.75 
65.88 
68.00 



2.18 
4.36 
6.54 
8.71 
10.89 
13.07 
15.25 
17.42 
19.61 
21.78 
23.96 
26.14 
28.32 
30.50 
32.67 
34.85 
37.03 
39.21 
41.39 
43.56 
45.75 
47.92 
50.10 
52.28 
54.46 
56.63 
58.81 
60.99 
63.17 
65.35 
67.52 
69.70 



2.23 
4.46 
6.70 
8.92 
11.16 
13.39 
15.62 
17.85 
20.08 
22.32 
24.54 
26.78 
29.00 
31.24 
33.48 
35.70 
37.92 
40.17 
42.40 
44.63 
46.86 
49.08 
51.32 
53.55 
55.78 
58.02 
60.24 
62.48 
64.70 
66.94 
69.18 
1.40 



I Of" 



W" 


\\\" 


2.45 


2.34 


2.39 


4.67 


4.79 


4.90 


7.02 


7.17 


7.32 


9.34 


9.57 


9.';8 


11.68 


11.95 


12.22 


14.03 


14.35 


14.68 


16.36 


16.74 


17.12 


18.70 


19.13 


19.55 


21.02 


21.51 


22.00 


23.38 


23.91 


24.44 


25.70 


26.30 


26.88 


28.05 


28.68 


29.33 


30.40 


31.08 


31.76 


32.72 


33.47 


34.21 


35.06 


35.86 


36.66 


37.40 


38.25 


39.10 


39.74 


40.64 


41.54 


42.08 


43.04 


44.00 


44.42 


45.42 


46.44 


46.76 


47.82 


48.88 


49.08 


50.20 


51.32 


51.42 


52.59 


53.76 


53.76 


54.99 


56.21 


56.10 


57.37 


58.65 


58.42 


59.76 


61.10 


60.78 


62.10 


63.54 


63.10 


64.5:. 


65.98 


65 45 166.9;!. 


68.4:5 


67.80 60.33 


70.86 


70.12,71.72 


73.31 


72.46,74.11 


75.76 


74.80 


76.50 


78.20 



\1\" \1\" I2|" 



42 



2.70 
5.41 
8.13 
10.84 
13.55 
16.26 
18.97 
21.67 
24.39 
27.09 
29.80 
32.52 
35.22 
37.93 
40.64 
43.35 
46.06 
48.77 
51.48 
54.19 
56.90 
59.60 
62.32 
65.03 
67.74 
70.44 
73.15 
75.87 
78.57 
81.28 
83.99 
86.70 



I08d 



METALS. — STEEL. 



Table 13c. 

WEIGHTS OF STEEL ANGLES. 

Per lineal foot in pounds. 





Thickness in Inches. 


Size in 




Inches. 


i 


3^. 


T^a 


/. 


k 


-A 


e 


in n 


'i-r n 


1Q A 


i 


23. C 
26.. ^ 


1 

24. S 

28.7 


ii 

26.8 
30.9 


1 


7 XS}4 




6 XO 
6 X4 
6 X3i^ 














14.4 17.2 19!6 


21.9 24.2 


28.7 
33 . 1 












.... 


V2.S 14.3 16.2 


18.1 


20.0 


21. h 


23. (j 


25 . 4 


27.2 














11.7 13.5 15.3 


17.lil8.9 


20. fc 


22.3 


:.M 




5 xr. 










25 . 7 














12.3 14.3 16.2 


18.1 


20.0 


21.8 


23.6 


25.4 


■-'7 . 2 


5 X4 






.... 


• . • • 1 . . . . 




11.0 12.8 14.5 


16. «' 


!l7.8 


19.5 


21.1 


22.6 


24.2 


5 X3l^ 
5 X3 
4^X3 








. . . 






10.4 12.0 13.6 


15.2 


'16. 8 


18.3 


19.8 


21.3 


2W.7 












8.2 


9.811.3 12.8 


14.2 


15.7:17.1 


18.5 


]d:t 
















9.1 10.5 11.9 


14.3 


14.0 


15.9 


17.2 


18.5 




4 X4 
4 X3i^ 
4 X3 

mx2% 


.... 




5.2 




'eie 


8^2 


9.8 


11 3 12.8 


14.3 


15.7 


17.1 


18.5 


19.9 
















9.1 


10.5 


11.9 


13.3 


11.6 


15.9 


17.2 


18 5 














7.1 
6.4 


8.5 
7.7 


9.8 

8.8 


11.1 
10.0 


12.3 
11.1 


13.6 
12.2 


14.8 
13.3 


16.0 
14.3 


jir.i 




33^x33^ 

33^X3 
33^x23^ 




3.7 






*5!7 


7.1 


8.5 


9.8 


11.1 


12.3 


13.6 


14.8 


16 C 


17 1 












4.9 


6.6 
G.l 


7.8 
7.2 
7.8 
6.2 
7.2 
.6 
5.9 


9.1 
8.3 
9.0 
7 '^ 


10.2 
9.4 

10.2 
8.1 
9.4 
8.5 


11.4 
10.4 
11.4 

9.0 
10.4 

9.5 


12.5 


13.6 


14.7 


15.7 




3^X3^ 
334x2 




'3:4 






4!3 


5 3 


11.4 
12.5 


12.4 
13.6 


14.7 






3 X3 
3 X23^ 


'2."g 








4.9 

4.5 


6!l 
5.5 


8^4 
7.6 
6.8 


11.4 


12.4 


13.4 


14.4 




3 X2 






'3!l 


3.6 


4^1 


510 












lY^^'W^ 


214 




3.5 




4.5 


5.5 


6.6 


7.6 


I'l 














23^X23^ 


2.1 




3.0 


3^6 


4.1 


5.0 


5.9 


6.8 




8.5 


9.3 


10.1 








234x2 






2.8 




3.7 


4.5 


5.3 


6.1 


6^8 














234x1% 






2.6 


. . . . 
























234x134 






2.4 




3.2 


'ii'.h 


4.6 


5.3 


6.0 














2^X234 


"i!9 




2.8 


. . . . 


3.7 


4.5 


5.3 


6.1 


QS 














2^X1^ 






2.3 





3.0 


3.7 


4.8 


5.0 


5J) 














2 X2 


i'.i 


. . . . 


2.5 




3.2 


4.0 


4.7 


5.3 
















2 XI34 






2.1 




2.8 


3.4 


4.0 


















2 y\% 






2.1 




2.7 


3.3 


3.8 


















mxm 


1.4 




2.1 




2.8 


3.i 


4.0 


4.6 
















WaX.iYo 






2.0 




2.6 


3.3 


3.9 


















iJ^xi34 


'i.*2 




1.8 




2.4 


2.9 


3.4 


















1%X1 


1.0 






1,6 
























1%X % 


1.0 




1.4 




'i!9 






















134X1H 


1.0 




1.5 




1.9 


2.4 




















1^X1^ 


0.9 




1.3 






i.l 




















1 XI 


0.8 




1.2 




1.5 






















1 X H 






1.0 


























1 X % 


0.7 




1.0 


























%x % 


0.7 




1.0 


























Ix i 


0.6 




0.8 


























0.5 































METALS. — STEEL. 



108e 



Table Idd, 

WEIGHTS AND DIMENSIONS OF STANDARD STEEL 



' I " BEAMS. 



Depth of 


Weight 
per Foot 


Area of 


Thickness of 


Width of 


Beam 


Section. 


Web 


Flange 


in Inches. 


in Pounds. 


Square Inches. 


in Inches. 


in Inches. 


3 


5.5 


1.63 


.17 


2.33 




6.5 


1.91 


.26 


2.42 




7.5 


2.21 


.36 


2.52 




7.5 


2.21 


.19 


2.66 




8.5 


2.50 


.26 


2.73 




9.5 


2.79 


.34 


2.81 




10.5 


3.09 


.41 


2.88 




9.75 


2.87 


.21 


3.00 




12.25 


3.60 


.36 


3.15 




14.75 


4.34 


.50 


3.29 




12.25 


3.61 


.23 


3.33 




14.75 


4.33 


.35 


3.45 




17.25 


5.07 


.47 


3.57 




15.00 


4.42 


.25 


3.66 




17.50 


5.15 


.35 


3.76 




20.00 


5.88 


.46 


3.87 




17.75 


5.33 


.27 


4.00 




20.25 


5.96 


.35 


4.08 




22.75 


6.69 


.44 


4.17 




25.25 


7.43 


.53 


4.26 




21.00 


6.31 


.29 


4.33 




25.00 


7.35 


.41 


4.45 




30.00 


8.82 


.57 


4.61 




35.00 


10.29 


.73 


4.77 


10 


25.00 


7,37 


.31 


4.66 




30.00 


8.82 


.45 


4.80 




35.00 


10.29 


.60 


4.95 




40.00 


11.76 


.75 


5.10 


12 


31.50 


9.26 


.35 


5.00 




35.00 


10.29 


.44 


5.09 




40.00 


11.76 


.56 


5.21 


15 


42.00 


12.48 


.41 


5.50 




45.00 


13.24 


.46 


5.55 




50.00 


14.71 


.56 


5.65 




55.00 


16.18 


.66 


5.75 




60.00 


17.65 


.75 


5.84 


18 


55.00 


15.93 


.46 


6.00 




60.00 


17.65 


.56 


6.10 




65.00 


19.12 


.64 


6.18 




70.00 


20.59 


.72 


6.26 


20 


65.00 


19.08 


.50 


6.25 




70.00 


20.59 


.58 


6.33 




75.00 


22.06 


,65 


6.40 


24 


80.00 


23.32 


.50 


7.00 




85.00 


25.00 


.57 


7.07 




90.00 


26.47 


.63 


7.13 




95.00 


27.94 


.69 


7.19 




100.00 


29.41 


.75 


7.25 



108/ 



METALS. — STEEL. 



Table 136. 

WEIGHTS AND DIMENSIONS OF STANDARD STEEL CHANNELS. 



Depth of 


Weigrht 


Area of 


Thickness 


Width of 


Channel 


V)er Foot 


Section, 


of Web 


Flange 


iu Inches. 


in Pounds. 


Square Inches. 


in Inches. 


in Inches. 


3 


4.0 


1.19 


.17 


1.41 


'' 


5.0 


1.47 


.26 


1.50 


it 


6.0 


1.76 


.36 


1.60 


4 


5.25 


1.55 


.18 


1.58 


ti 


6.25 


1.84 


.25 


1.65 


(I 


7.25 


2.13 


.33 


1.73 


5 


6.50 


1.95 


.19 


1.75 


tt 


9.00 


2.65 


.33 


1.89 


t( 


11.50 


3.38 


.48 


2.04 


6 


8.00 


2.38 


.20 


1.92 


ft 


10.50 


3.09 


.32 


2.04 


if 


13.00 


3.82 


.44 


2.16 


n 


15.50 


4.56 


.56 


2.28 


T 


9.75 


2.85 


.21 


2.09 


<« 


12.25 


3.60 


.32 


2.20 


(( 


14.75 


4.34 


.42 


2.30 


** 


17.25 


5.07 


.53 


2.41 


<( 


19.75 


5.81 


.63 


2.51 


8 


11.25 


3.35 


.22 


2.26 


it 


13.75 


4.04 


.31 


2.35 


ti 


16.25 


4.78 


.40 


2.44 


ti 


18.75 


5.51 


.49 


2.53 


*t 


21.25 


6.25 


.58 


2.62 


9 


13.25 


3.89 


.23 


2.43 


(( 


15.00 


4.41 


.29 


2.49 


i< 


20.00 


5.88 


.45 


2.65 


tt 


25.00 


7.35 


.61 


2.81 


lO 


15.00 


4.46 


.24 


2.60 


'* 


20.00 


5.88 


.38 


2.74 


n 


25.00 


7.35 


.53 


2.89 


(f 


30.00 


8.82 


.68 


3.04 


€t 


35.00 


10.29 


.82 


3.18 


12 


20.50 


6,03 


.28 


2.94 


< ( 


25.00 


7.35 


.39 


3.05 


(( 


30.00 


8.82 


.51 


3.17 


(< 


35.00 


10.29 


.64 


3.30 


(( 


40.00 


11.76 


.76 


3.42 


15 


33.00 


9.90 


.40 


3.40 


ft 


35.00 


10.29 


.43 


3.43 


<{ 


40.00 


11.76 


.52 


3.52 


it 


45.00 


13.24 


.62 


3.62 


** 


50.00 


14.71 


.72 


3.72 


4 t 


55.00 


16.18 


.82 . 


3.82 



METALS. — STEEL. 



108^ 



Table 13/. 
WEIGHTS AND DIMENSIONS OF STANDARD STEEL TEES. 



Width of 


Depth of 


Thickness of 


Thickness of 


Weight 


Area of 
Section 


Fi u.ge 


Bar 


Flange 


Stem 


per Foot 


in Square 
Inches. 


in Inches. 


in Inches. 


in Inches. 


in Inches. 


in Pounds. 


1 


1 


1/8 to 5/32 


1/8 to 5/32 


0.89 


.26 


n 


li 


3/16 ''7/32 


5/32 "7/32 


1.39 


.41 


h\ 


lA 


3/16 '' 1/4 


5/32 ' ' 7/82 


1.53 


.45 


n 


li 


3/16 ''1/4: 


5/32 " 1/4 


1.61 


.47 


n 


1- 


3/16 "1/4 


5/32 " 1/4 


1.85 


.54 


2 


2 


1/4 *' 5/16 


1/4 " 5/16 


3.70 


1.05 


2 


2 


5/16 ** 3/8 


5/16 *• 3/8 


4.30 


1.26 


H 


H 


1/4^' 5/16 


1/4 " 5/16 


4.10 


1.19 


3 


3 


3/8 '^7/16 


3/8 " 7/16 


7.80 


2.27 


H 


Bi 


3/8 ** 7/16 


3/8 " 7/16 


9.30 


2.74 



1087^ 



METALS. — STEEL. 



Table 18^. 

WEIGHTS AND DIMENSIONS OF STEEL "Z" BARS. 



Depth of 


Lengjth of 


Thickness of 
Web and 


Weight 


Area of 


Bar 


Legs 


liegrs 
in Inches. 


per Foot 


Section. 


in Inches. 


in Inches. 


in Pounds. 


Square Inches. 


3 


m 


1/4 


6.7 


1.97 


3iV 


2| 


5/16 


8.4 


2.48 


3 


Sri 


3/8 


9.7 


2.86 


3A 


3y 


7/16 


11.4 


3.36 


3 


8-1 


1/2 


12.5 


3.69 


3tV 


3| 


9/16 


14.2 


4.18 


4 


3A 


1/4 


8.2 


2.41 


4tV 


Si 


5/16 


10.3 


3.03 


^ 


3A 


3/8 


12.4 


3 66 


4 


3iV 


7/16 


13.8 


4.05 


tf 


H 


1/2 


15.8 


4.66 


h\ 


9/16 


17.9 


5.27 


4 


3tV 


5/8 


18.9 


5.55 


4A 


31 


11/16 


20.9 


6.14 


4i 


3A 


3/4 


23.0 


6.75 


5 


3i 


5/16 


11.6 


3.40 


5t\ 


3tV 


3/8 


13.9 


4.10 


5i 


31 


7/16 


16.4 


4.81 


5 


3i 


1/2 


17.9 


5.25 


5,V 


3A 


9/16 


20.2 


5.94 


5J 


31 


5/8 


22.6 


6.64 


5 


H 


11/16 


23.7 


6.96 


5xV 


3A 


3/4 


26.0 


7.64 


5^ 


81 


13/16 


28.3 


8.33 


6 


3i 


3/8 


15.6 


4.59 


6tV 


3A 


7/16 


18.3 


5.39 


6J 


3| 


1/2 


21.0 


6.19 


6 


3i 


9/16 


22.7 


6.68 


6tV 


3tV 


5/8 


25.4 


7.46 


6i 


3f 


11/16 


28.1 


8.25 


6 


3i 


3/4 


29.3 


8.63 


6tV 


3A 


13/16 


31.9 


9.39 


6i 


31 


7/8 


34.6 


10.17 



METALS. — STEEL. 109 



Steel. 



Steel has a chemical composition intermediate between cast 
iron and wrought iron. It is produced either by adding carbon to 
wrought iron, or by partly removing carbon from pig iron. 

Steel is generally distinguished from both cast and wrought 
iron by the property of tempering which it possesses ; that is to 
say, it can be hardened by sudden cooling from a high tempera- 
ture, and its degree of hardness or softness can be regulated with 
precision by suitably fixing the temperature. But with the soft 
steels now produced this property is no longer a distinguishing 
sign, as many of them will not take a temper. 

Steel may be distinguished from wrought iron by placing a 
drop of nitric acid upon it. If a dark-gray stain is produced it is 
steel. 

Yakieties of Steel. 

Steel is made by many processes, of which the following are 
the most important : 

Blister Steel is made by a process called cementation, in 
which bars of the purest wrought iron are embedded in layers of 
charcoal, and subjected for several days to a high temperature. 
Each bar absorbs carbon, and its surface becomes converted into 
steel, while the interior is in a condition intermediate between steel 
and iron. The steel receives its name from blisters which appear 
upon the surface : when these are small in size and are regularly 
distributed, the steel is of good quality ; when they are large and 
irregularly distributed, it indicates a want of homogeneity in the 
iron used. 

Blister steel cannot be used for ordinary forging, nor for cutting 
tools. It is used for facing hammers and for making other varie- 
ties of steel. 

Shear Steel is made by breaking bars of blister steel into 
short lengths, making them into bundles, sprinkling with borax 
and sand, and heating them to a welding heat, then rolling or 
hammering them until a near approach to uniformity of compo- 
sition and texture has been obtained. The product is termed single- 
shear steel, and if repeated the product is termed double-shear 
steel. It is used for various tools and cutting implements. 

Puddled Steel is produced by stopping the puddling process 
in the manufacture of wrought iron before all the carbon has 
been removed. It is of inferior quality, used for making plates 
for ship-building. 



110 METALS. — STEEL. 

A similar product resulting from imperfect refining is kuown 
as Natural Steel or German Steel. 

Bessemer Pkocess. — In this process pig iron of a dark-gray 
color, containing a large proportion of carbon, with but a small 
percentage of silicon and manganese and practically no sulphur 
and phosphorus, is melted in a cupola, or run direct from the 
blast-furnace into a ''converter," which is a pear-shaped vessel 
lined with fire-brick, while in the converter a strong blast of air 
is forced through the molten metal for about twenty minutes. 
The color of the flame indicates to the experienced eye when all 
the carbon is removed, or more accurately determined by means 
of a spectroscope. Then from 5 to 10 per cent of spiegeleisen is 
added. The molten metal is again agitated by the air-blast, and 
when the two metals are thoroughly incorporated the steel is run 
into ladles and thence into the moulds. The ingots thus obtained 
are not as compact as required, but are made so by hammering. 
They are then rolled into the desired sizes and shapes for use. 

The Basic Process is similar to the preceding. The con- 
verters are lined with magnesian limestone or some refractory 
substance which contains practically no silica. In this process 
the silicon, carbon, and phosphorus are removed. 

Siemens or Open-hearth Process. — In this process pig 
iron and ore are fused on the open hearth of a regenerative gas 
furnace. The pig iron is first melted and raised to a temperature 
which will melt steel; rich and pure ore and limestone are added 
gradually. The chemical reactions convert the silicon into silicic 
acid, which forms a fusible slag with the lime, and the carbon 
passes off as carbonic acid. A modification of this process con- 
sists in treating the iron ore in a rotary furnace with carbonaceous 
matter, by which both sulphur and phosphorus are removed. 

Siemens-Martin Process. — In this process a bath of highly 
heated pig iron is prepared in a furnace, and three or four times 
its weight of scrap-iron and steel are added and dissolved in the bath 
with enough ore to reduce the carbon to about 0.1 per cent. The 
furnace then contains a fluid malleable iron, to which is added 
silicious iron, spiegeleisen, ov ferro-manganese in such proportions 
as are necessary to produce a steel of the requisite hardness. 

The open-hearth processes require from 7 to 10 hours for one 
heat, while the Bessemer blow can be made in about half an 
hour. 

The terms acid and basic process refer to the character of the 
lining of the converter or hearth of the furnace— aac^ signifying 



METALS. — STEEL. Ill 

that a silicious material, as sandstone or quartz, is used for the 
lining, and basic that lime and magnesia as existing in calcined 
dolomite are used. There are diverse opinions as to the relative 
values of steel made by the acid and basic processes. In the acid 
open hearth process the stock used is usually very low in phos- 
phorus at the start. 

The terms " Bessemer " and *' open-hearth " steels have refer- 
ence to methods and processes, and not to qualities. 

Cast Steel is produced by various processes, either by melt- 
ing fragments of steel produced by any of the other processes, 
or by melting wrought iron made from the purer magnetic ores 
with carbon, spiegeleisen, oxide of manganese, etc. 

Cast steel is strong and hard, can be forged but not welded 
(made by Heath's process it is capable of being welded to other 
portions of the same material or to wrought iron). If raised be- 
yond a red heat it becomes brittle. 

Blow-holes may be diminished if not entirely prevented by the 
addition of manganese and silicon in sufficient quantities, but 
both of these cause brittleness. 



Classification of Steel. 

For convenient distinguishing terms, it is customary to classify 
steel in three grades, viz., *'mild or soft," *' medium,'* and 
" hard " ; and although the different grades blend into each other 
so that no line of distinction exists, in a general sense the grades 
below 0.15 per cent carbon are considered as ''soft," from 0.15 
to 0.30 per cent carbon as ** medium," and above 0.30 per cent of 
carbon as " hard." Each grade has its own advantages for the 
particular purpose to which it is adapted. 

The soft steel is well adapted for boiler-plate and similar 
purposes, where its high ductility is advantageous. The medium 
grades are used for general structural purposes, while the hard 
grades are especially adapted for axles and shafts, and any ser- 
vice where good wearing surfaces are desired. Plate steel is 
usually graded as follows : 

Tank Steel (the cheapest).— Hard and brittle; also steel plates 
rejected from the higher grades. 

Shell Steel. — Soft steel, usually made by the open-hearth 
process, and used for boilers, stand-pipes, etc. 

FLANaB Steel.— A superior quality of soft steel. 



112 METALS. — STEEL. 

Ordinary Fire-box Steel iind Locomotive Fire-box 
Steel are high grades of soft steel possessing special properties 
which fit them for the use indicated by their trade designation. 



I 



Properties of Steel. 

Specific Gravity. — Average 7.854. The specific gravity of 
steel is influenced not only by its chemical constituents, but by 
the heat to which it is subjected, and also according to the de- 
gree of condensation imparted by the process of rolling or forg- 
ing. The average given above has been adopted as the result of 
a uumber of careful experiments. 

Weight per Cubic Foot, 490 Lbs. — This figure is taken for 
convenience. The weight is affected by the same causes stated 
under specific gravity, and varies from 489.6 to 489.77. A 
weight extensively used is 489.6 lbs. per cubic foot, or about 2 
per cent more than wrought iron. 

Melting-point.— Soft steel, 2372° to 2542° F.; hard steel, 
2570° F.; mild steel, 2687° F. 

Specific Heat, .1165. 

Conductivity of Heat, 11.6. 

Conductivity of Electricity, 12 (silver being 100). 

Expansion and Contraction. — Expansion per degree Fahr. 
per unit of length = 0000064, or ^ inch in 1575 ft. For a varia- 
tion in temperature of 100 degrees F. the change in length will 
be about one inch in 125 feet. 

Extension is about .1 inch in 111 feet for every ton per 
square inch of load. 

Strength of Steel. — The strength of steel depends largely 
on the amount of the constituent elements that are associated with 
the iron, and each of which affects more or less the hardness and 
strength of the metal. 

The principal of these are carbon, manganese, silicon, phos- 
phorus, and sulphur. The first named is purposely retained as 
useful or necessary; the others are rejected, as far as practicable, 
as objectionable when in excess of certain minute proportions. 

The tensile strength ranges from 25,000 to 180,000 lbs per square 
inch ; it is increased by reheating and rolling up to the second 
operation, biit decreases after that. 

As a general rule, the percentage of carbon in steel determines 
its hardness and strength. The higher the carbon the harder the 
steel, the higher the tenacity, and the lower the ductility will be. 



METALS. — STEEL. 



113 



The following table exhibits the average physical properties of 
good open -hearth steel: 



Table 14. 

PHYSICAL PROPERTIES OF OPEN HEARTH BASIC STEEL. 







Tensile Strength. 
Lbs. per Square Inch, 


Ductility. 




Percentage 
of 








Grade. 












Carbon. 


Ultimate 


Elastic 


Elongation 


Reduction 
of Frac- 
tured Area. 






Strength. 


Limit. 


in 8 Inches. 










per cent. 


per ( ent. 


Soft 


.08 


54,000 


32,500 


32 


60 


<( 


.09 


54,800 


33,000 


31 


58 


it 


.10 


55,700 


33,500 


31 


57 


ft 


.11 


56,500 


34,000 


30 


56 


€l 


.12 


57,400 


34,500 


30 


55 


it 


.13 


58,200 


35,000 


29 


54 


l( 


14 


59.100 


35,500 


29 


53 


Medium . . . 


.15 


60,000 


36,000 


28 


52 


'< 


.16 


60,800 


36,500 


28 


51 


(( 


.17 


61,600 


37,000 


27 


50 


It 


.18 


62,500 


37,500 


27 


49 


'* . . . . 


.19 


63,300 


38,000 


26 


48 


(( 


.20 


64,200 


38,500 


26 


47 


*t 


.21 


65,000 


39,000 


25 


46 


(I 


.22 


65,800 


39,500 


25 


45 


it 


.23 


66,600 


40,000 


24 


44 


** . . . . 


.24 


67,400 


40,500 


24 


43 


<( 


.25 


68,200 


41,000 


23 


42 


tt 


.30 


77,000 


46,000 


20 


35 


Hard :. 


.35 


82,000 


49,000 


18 


30 


«< 


.40 


87,000 


52,000 


16 


25 



Working Strength in tension members is usually taken at 
16,000 lbs. per square inch for angles and channels, and at 18,000 
lbs. for round or flat bars. For columns the compression strain 
is taken at from 12,000 to 14,000 lbs. per square inch of section 
when the length is less than 90 radii. 

Tenacity at High Temperatures.— The strength of steel 
diminishes as the temperature increases from 0° until a minimum 
is reached between 200° and 300° F , the total decrease being about 
4000 lbs persquare incli in the softer steels, ar.d from GOOO to 8000 
lbs. in steels of over 80,000 lbs. tensile stiength. Fiom this mini- 
mum point the strength increases up to a leniperalure of 400° to 



1 14 METALS. — STEEL. 

600° F., the maximum being reached earlier in the harder steefs, 
the increase amounting to from 10,000 to 20,000 lbs. per square 
inch above the minimum strength at from 200° to 300°. From 
this maximum the strength of all steel decreases steadily at a 
rate approximating 10,000 lbs. decrease per 100° increase of tem- 
perature. A strength of 20,000 lbs. per square inch is still shown 
by steel containing 0.10 carbon at about 1000° F., and by steel con- 
taining 0.60 to 1.00 carbon at about 1600° F. 

Strength of Welds. — 

Strength of solid bar 54.226 to 64.580 lbs. per square inch 

" welded bar, .. . 28.553 to 46.019 '* '' 

Mild steel has superior welding property as compared to hard 
steel, and will endure higher heat without injury. 

Hardening. — Steel containing about .40^ carbon will usually 
harden sufficiently to cut soft iron and maintain an edge. 

Steel Alloys. 

Manganese, Nickel, Chrome, and Tungsten Steels are 
made by adding a small percentage of the metals named to the 
molten steel, the result in each case being a steel of great hard- 
ness and tenacity. 

Manganese steel is very free from blow-holes ; it welds with 
great difficulty; its toughness is increased by quenching from 
a yellow heat; its electric resistance is enormous, and very 
constant with changing temperature. It is low in thermal 
conductivity. Its great hardness cannot be materially less* 
ened by annealing. At a yellow heat it may be forged read- 
ily, but at a bright red heat it crumbles under the hammer. But 
it offers great resistance to deformation, i.e., it is harder when hot 
than carbon steel. 

Nickel steel possesses great tensile strength and ductility, high 
elastic limit and homogeneity, great resistance to cracking, a prop- 
erty to which the name non-fissihility has been given. It forges 
readily, whether it contains much or little nickel. If the propor- 
tion of nickel rises above 5^, cold working becomes difficult. 

The tensile strength of forged bars containing 3{^ nickel ranges 
from 105,300 to 276,800 lbs. persq. in.; of rolled bars, from 86,000 
to 143,000 lbs. per sq. in. Tl)e strength of rolled bars containing 
"11% nickel ranges from 102,000 to 1 18,000 lbs. persq. in. With 
27^ of nickel the steel is practically non corrodible and non-inag- 
nelic. 



METALS. — STEEL. 1 15 

Chrome and Tungsten Steel are made by adding a small 
percentage of cbromium or tungsten to steel, the result pro- 
ducing a steel of great hardness and tenacity. 

Alloys of steel with silver, platinum, aluminum, etc., are made 
with the view of improving the fabrication of the finer grades of 
surgical and other instruments. 

Compressed Steel. — In the Whitworth process steel is sub- 
jected to compression while fluid under a pressure of from 4 to 
12 tons per square inch. The pressure is applied and increased 
gradually Within half an hour or less after the application of 
the pressure the column of fluid steel is shortened 1-| inches per 
foot, or about one eighth of its length; the pressure is kept on 
for several hours, th^ result being that the metal is compressed 
into a perfectly solid and homogeneous mass, free from blow- 
holes. 

Terms used in Steel-working*. 

Bled Ingots. — Ingots from the centre of which molten steel 
has escaped, leaving a cavity. 

Burned Steel. — Steel that has been partly reduced to oxide 
by overheating. 

Check. — A small rupture caused by water. It may run in 
any direction. It is usually invisible until the steel is ruptured. 

Chemical Numeration. — The chemical quantities of carbon, 
etc., are expressed in hundredths of one percent. In the mill 
the steel is spoken of as 20 or 50 carbon, or 8 phosphorus, or 10, 
15, or 25 silicon, etc., meaning that the steel contains twenty 
hundredths of one per cent of carbon, etc. 

Dead melting (synonym, killing) means melting steel in the 
crucible or open hearth until it ceases to boil or evolve gases. It 
is then dead, — it lies quiet in the furnace, — and, killed properly, 
it will set in the moulds without rising or boiling. 

Grade applies to quality— as crucible, Bessemer, or open- 
hearth grade; or, in the crucible, common spring, tool, special 
tool, machinery, etc., etc. It does not indicate temper or relative 
hardness. 

Overblown. — Steel that has been blown in a Bessemer con- 
verter after the carbon is all burned; then there is nothing but 
steel to burn, and the icsiilt is bad. 

Overheated. — Stccl that Iims been heated too hot: its fipry 
fracture exposes it. The grain of ovci heated steel \ui\y be re- 



1 1^6 METALS. — STEEL. 

Stored, but restored steel is never as reliable as steel that has not 
been overheated. Overheating is a disintegrating operation. 

OvERMELTED.— Steel that has been kept too long in fusion. 
The finest material may be ruined by being kept in the furnace 
any considerable time after it has been killed. 

Point.— One hundredth of one per cent of any element, as 10 
points of carbon, or 10 carbon, etc. 

Recalescence.— The name given to the phenomenon which 
occurs when a piece of steel is heated above medium orange and 
allowed to cool slowly. 

Restoring.— The operation of reheating overheated steel and 
allowing it to cool slowly, by which operation its grain becomes 
fine and its fiery lustre disappears. 

Short (Cold, Red, Hot). — Cold-short steel is weak and brittle 
when cold. 

Red-short steel is brittle at dark-orange or medium-orange heat 
or at the common cherry-red. It may forge well at a lemon 
heat, and be reasonably tough when cold. 

HoUshort steel is brittle and friable above a medium-orange 
color. It may forge well from medium orange down to black 
heat. 

Temper.— Used by the steel-maker, it means the quantity of 
carbon present. It is low temper, medium, or high, or number 
so. and so by his shop numbers. 

Used, by the steel user or the temperer, it means the color to 
which hardened steel is drawn— straw, brown, pigeon-wing, 
bjue, etc., etc. 

Or, it is the Steel-maker's measure of initial hardness, and it is 
the steel-user's measure of final harduess. 

Watek-crack.— A crack caused in hardening ; it may run in 
any direction governed by lines of stress in the mass. It is dis- 
ti,nguished from a check by being larger, and usually plainly 
vi.sible. 

Wild Steel.— Steel in fusion that boils violently, and acts in 
the moulds as lively soda-water or beer does when poured into 
a glass. 



METALS.— STEEL. 117 



Mill Inspection of Steel. 

Steel Ingots are examined to discover the following defects : 

Blow-holes or cavities caused by the escape of gas evolved 
during cooling and solidification. These under some conditions of 
melting and composition occur throughout the mass, but espe* 
cially near the surface and toward the upper part of the ingot. 

Pipe.— A cavity caused by the outside of the ingot cooling more 
rapidly than the inside. This defect usually concentrates within 
conical lines in about the upper third of the ingot, but may occur 
anywhere by bad teeming. 

External Ckacks caused by the rapid shrinkage of the out- 
side or skin of the ingot, and at times due to hydrostatic pressure 
of the internal and fluid portion. 

Internal Cracks due to interior strains set up by too rapid 
cooling, and occurring most frequently in ingots of hard steel. 

Segregation. — The separating and gathering together by 
themselves during cooling of certain chemical constituents — nota 
bly phosphorus, sulphur, and carbon, and to a less degree silicon 
and manganese. The segregation is generally toward the central 
and upper portion of the ingot, where cooling and solidification oC 
the metal last takes place. The selection of the most highly segre^- 
gated spots for analysis will give a knowledge of the worst possi- 
ble condition of the metal. In order to avoid extreme segregation 
no ingot should be cast of a greater weight than 15,000 pounds. 

Ingots should be bottom cast, and should not be disturbed or 
moved from the position in which they are cast until sufficiently 
solidified to preclude '* bleeding. '* Bled ingots and ingots not 
bottom cast should be rejected. 

The inspector of ingots should note especially casts that have 
been too violently or quickly melted or burnt, and report the 
same, so that steel rolled therefrom may be subjected to special 
examination. 

Appearance op Good Steel. — The appearance of the fresh 
fracture of an ingot will give an indication of the quality of the 
steel. If the color be a bluish gray, with uniform grain, slight 
lustre, and silky appearance, it is an indication of good steel, and 
the steel-worker will say that it is *' sappy "—meaning that it is 
just right. If the fracture be dull and sandy looking, without 
lustre or sheen, and without the bluish cast or having more of 
a shade of yellowish sandstone, it is an indication of impurity and 



118 METALS. — STEEL. 

weakness, aud the steel-worker will say it is *'dry." If th 
fracture be granular, with bright flashiug lustre, the steel-worker 
will say it is " fiery/' This condition is an evidence of high heat. 
If ihe grain be fairly fine and of a bluish cast, it is not neces- 
sarily bad. In mild steel, in high sleel, or in tool steel it shoultj 
not be tolerated. If the grain be large aud of a brassy cast, it is 
an evidence of bad condition. The grain should be restored be^ 
fore the steel is used. In hardened steel it is always bad, except 
in dies to be used under the impact of the drop-hammer; in this 
case steel must be so hard as to be slightly fiery. 

The quality of the steel from each heat or blow is ascertained 
by testing specimens obtained by casting small billets about 4 in. 
square and rolling them down into a f-in. round. 

These tests will usually run a little below the final finished 
material tests in elastic limit and ultimate strength, and a little 
above them in elongation and reduction. Allowance should be 
made for this variation in the acceptance of the heat. 

The amount of phosphorus, etc., is determined from the 
same billets before the ingots are rolled, or from drillings taken 
directly from one of the ingots. 

The samples for chemical analysis should be sent to the labora- 
tory without unnecessary delay. 

Marking Ingots. — Each ingot should be marked plainly with 
its melt number, and this melt number must be stamped or 
painted on all blooms, billets, or slabs made from such ingots, in 
order to identify the material through its various processes of 
manufacture, aud the melt number, together with the furnace- 
heat number, must be plainly marked on each piece of finished 
material. 

Melt Records. — A complete record of each melt should be 
kept, showing character of the raw materials, the number, size, 
and weight of each ingot cast, the number of ingots rejected, 
and the reasons therefor. 

Rolled Steel. — When the rolling is made the inspector 
should be on hand to see that the bars are of the required size 
and free from defects; at the same time he should select the test- 
pieces. 

The defects causing rejection of rolled steel are as follows : 

Blow-iioles aud Pipes caused by the non-removal of these 
defects from tiu; ingot. 

Stakb. — Briliiiint spols in mid section showing that the pipe 
was n(;t all cut away from the ingot. 



METALS. — STEEL. 119 

Pits. — Caused by burning; they occur in the form of snnjill 
cup-like holes, and must not be confounded with cinder spots. 

Cinder Spots are due to pieces of cinder or fire-brick being 
rolled into the metal. 

Cracks. — Due to rolled-out blow-holes. If a bar, plate, or 
beam shows cracks on the surface or at the corners, with rough, 
torn surfaces, the steel has either been superficially burned or it 
is red-short. In either case it should be rejected, for the ci-acks, 
although they may be small, will provide starting-points for ulti- 
mate fractures. 

Laps or Laminations. — A lap or lamination is caused by care- 
less hammering, or by badly proportioned grooves in rolls, or by 
careless rolling. A portion of the steel is folded over itself, the 
walls are oxidized and cannot unite. A lap generally runs clear 
along a bar practically parallel with its axis; it is easily seen. 

Seams. — A seam is a longer or shorter defect caused by a 
blow-hole which working has brought to the surface and not 
eliminated. It usuall}^ runs in the direction of working. Seams 
are distinguished from laps by not being continuous; they are 
usually only an inch or two in length. 

Snakes are small lines twisting in every direction due to foreign 
substances in the heat separating two masses of pure steel. 

Cobbles are irregularities due to one side being heated more 
than another. 

Appearance of Fractured Surface. — The appearance of 
the fractured surface of steel is by many persons considered an 
index to the quality. With great experience on the part of the 
observer it may serve as a guide, but as a rule it is vague and 
uncertain. 

The appearance of the fracture is influenced by the manner in 
which the metal is broken. When rupture takes place slowly the 
fracture presents a silky fibrous appearance with an angular and 
irregular outline. When ruptured suddenly the fracture presents 
a granular appearance with the surface usually even and at right 
angles to the length. 

The color is a light pearl-gray, slightly varying in shade with 
the quality; the granular fractures are usually almost free from 
lustre, and, consequently, totally unlike the brilliant crystalline 
appearance of wrought iron. 

The last highest temperature to which steel was subjected can 
be very closely judged by the appear nee of a cold fracture. 



120 METALS. —STEEL. 

If the heating aud working were uniform the fracture will 
show an even grain throughout. 

A proper heat is indicated by a fine lustreless grain with a 
steely blue or gray color. 

Too high heat is indicated by a coarse lustrousless grain with 
a yellowish cast. * 

Too low a temperature is shown by a fine grain of a black or 
decided blackish color. 

Uneven heating or working, or both, is shown by an uneven 
grain. 

If the outside be fine-grained and the centre part be coarse 
aud fiery it shows high initial heat modified by superficial and 
msufficient working, either under the hammer or in the rolls. 

If the inside be fine-grained and the outside be coarse and 
fiery it shows that the last heat was too high, too quick and 
superficial. 

If the corners be coarse and fiery and the body of the piece be 
of proper grain it shows carelessness in heating, allowing the 
corners of the piece to run up much hotter than the body. 

The fracture of burned steel has a whitish hue, the crystals 
show bright and fiery, and show distinct, well-defined faces, 
whether large or small, and the granular or crystalline appear- 
ance of the fracture is very marked aud coarse. 

The nicked bending fracture of soft steel not burned will have 
a bluish-gray hue, with the structure not sharply defined or even 
" mushy " in appearance. 

Steel for Boileus. — In selecting steel for boilers, especially 
for locomotive boilers, the inspector should look for a peculiar 
marking which wull appear on the test-pieces if the metal has the 
desired quality. This marking consists of a series of faint lines 
running criss-cross and intersecting at the same angle. Some 
call it the skeleton of the steel. When this marking is found in 
an open-hearth steel specimen, and the other results of the test 
are satisfactory, the inspector may rest assured that the metal is 
of suitable quality for boilers. Why steel with this marking 
should give good results no one knows, but many years of expe- 
rience and investigation have shown it to be the case. If the steel 
is entirely uniform and the test-piece shows no marking of any 
kind it is unsuited for boilers. It will crack and break, and 
become "mushy" or homyconibcd. Good boiler steel should 
noi show a sudden rcdnciion jil ihc fi:iclnre, there should be n 
gradual reduction, and the occurrence of even a slight shoulder 



I 



METALS. — STEEL. 121 

on the contracted part should cause the steel to be looked on with 
suspicion. 

Steel Castings.. — The defects to be looked for in steel cast- 
ings are blow-holes, shrinkage- cavities, pits, and cracks. 

Appearance of Fracture.— The fracture of cast steel should 
have a slaty-gray tint, almost without lustre, the crystals being 
so fine that they are hardly distinguishable. 

The behavior of an unannealed steel casting resembles that of 
an overheated forging ; its chief characteristic is its brittleness 
when subjected to shock. Hard castings have this property to 
such a marked degree that sinking-heads are often broken off by 
the shock of chipping off the runner. 

The strains caused by shrinkage in cooling are frequently so 
great as to cause rupture. 

Shrinkage of Steel Castings. — In steel castings the amount 
of shrinkage varies with the composition and the heat of the 
metal ; the hotter the metal the greater the shrinkage. 

The allowance for shrinkage is from j^ to ^ inch per foot in 
length, except in very heavy castings, where ^ inch is sufficient, 
and ^ inch for finish on all machined surfaces, except such as are 
cast "up." Cope surfaces which are to be machined should, in 
large or hard castings, have an allowance of from | to J inch 
for finish, as a large mass of metal slowly rising in a mould is apt 
to become crusty on the surface, and such a crust is sure to be 
full of imperfections. On small, soft castings ^ inch on drag side 
and J inch on cope side will be sufficient. No core should have 
less than |-inch finish on a side, and very large ones should have 
as much as J-inch on a side. 

Specifications for Steel Castings (U. S. Navy Depart- 
ment). — Steel for castings must be made by either the open-hearth 
or crucible process, and must not show more than 0.06 of phos- 
phorus. All castings must be annealed unless otherwise directed. 

The tensile strength of steel castings shall be at least 60,000 
lbs., with an elongation of at least 15 per cent in 8 inches for all 
castings for moving parts of machinery and at least 10 per cent 
in 8 inches for other castings. Bars 1 inch square shall be capable 
of bending cold, without fracture, through an angle of 90° over a 
radius not greater than 1^ inches. All castings must be sound, 
free from injurious roughness, sponginess, pitting, shrinkage, or 
other cracks, cavities, etc. 

The test-strip should be poured along with the casting ; its 
dimensions should be } inch square by 12 inches long. 



122 METALS. — STEEL. 

Checking and Marking Accepted Material. — In tbe mill 

inspection of iron and steel tbe inspector should have a copy of 
the mill order and check off such as he accepts, so that he as well 
as the mill people may know how much remains to be done. 

Every accepted piece of material should be marked with a dis- 
tinguishiug mark. (The best form of marking-tool is a small 
steel hammer with a mark cut on one end ) The imprint on the 
metal should be surrounded by a ring of white paint so as to be 
readily seen. To the shopmen this stamp should be the signal 
that they can proceed with the required shop manipulations 
without asking questions. 

Tests for Steel. 

The tests to which steel is subjected are rhuch more rigid than 
for wrought iron destined for similar purposes. The reasons 
for this are that the acceptable qualities of one melt of steel 
offer no absolute guarantee that the next following melt from 
the same stock will be equally satisfactory. Moreover, steel is 
much more affected in the various processes of hardening, cold- 
rolling, overheating, etc., than iron. While soft steel of good 
quality is for many purposes a safe and satisfactory substitute 
for wrought iron, a poor steel or an unsuitable grade of steel is 
a dangerous substitute, for it may range from the brittleness of 
glass to a ductility greater than that of wrought iron. 

The tests usually prescribed by specifications to determine the 
quality of steel are : 

Tensile Tests, including the elastic limit and ultimate 
strength as measures of tenacity, together with the percentage of 
elongation and reduction of area as measures of ductility ; also 
bending, drifting, and forging tests, and chemical analysis to 
determine percentage of phosphorus, etc. 

The number of tests to be made will depend upon circum- 
s'ances and the specific instructions given by the engineer. Com- 
mon requirements are that a test-bar must be rolled from every 
melt, and that three tests of each kind shall be made from differ- 
ent ingots of each melt. 

Bending Test (iZbO- — Test-pieces of medium steel when 
heated to a cherry-red and cooled in water at 70° F. shall bend 
180 degrees round a circle whose diameter is equal to the thick- 
ness of the test-piece, without showing signs of ciacking on the 
convex side of the curve. 



METALS. — STEEL. 123 

Bending Test {Gold), — Specimens of rivet or soft steel shall 
bend cold through 180 degrees, and close down flat upon them- 
selves without cracking. 

If material of various shapes is to be made from the same melt 
the specimens for testing are to be so selected as to represent the 
different shapes rolled. 

Bending tests are usually made on ^it strips one inch wide 
and of the finished thickness of the metal, on round rods as they 
come from the rolls. 

DRiFTiNa Test. — Made by striking with a sledge upon a steel 
drift-pin in punched holes and noting the size to which these 
holes can be enlarged under different circumstances without 
fracture of the material. 

A hole punched for a f -inch rivet, its centre being 1^ inches 
from the rolled or planed edge, is required to be capable of en- 
largement in this way without fracture of the metal until it will 
pass a rod of the diameter of 1 inch for wrought iron, \\ inches 
for bridge steel, and 1 J inches for boiler-plate steel. 

The test-piece should be supported on the under side by a sur- 
face having a hole with a rounded edge, slightly larger than the 
punched hole to start with, and the size of holes increased as the 
drift-pin is driven through. Blank nuts make a very good sup- 
port. 

The drift-pin in starting should be entered from the lower side 
of the punched hole on account of the taper in the hole and in 
order that the fin left in punching may be drawn in by the drift- 
pin. 

The results of this test are affected by the w^eight of the sledge, 
the number of blows, the height of fall and rapidity of the blows, 
all of which should be noted and recorded. 

Hardening Tests. — These are made by heating a test piece 
to a red heat and plunging into water at 32° to 40° F. ; the piece 
is then bent and the results compared with those on a similar 
piece not hardened. 

Forging Test. — This test is chiefly used for rivet-rods. A 
part of the rod is brought to a fair red heat and hammered until 
cracks barely begin to show at the edge of the piece. The amount 
of flattening which the piece stands before cracks appear shows 
the red-shortness of the material. 

Welding Test. — A piece of metal with section about 1 inch 
in largest dimension is to be prepared for a single scarf-weld and 
heated ia a reducing flame io a clct^n fire, At a v^hite heat it 13 



124 METALS. — STEEL. 

to be removed and welded with an 8- to 10-lb. hammer, then upset 
while still hot, and finally drawn down under the hammer to its 
original size. No tiux and no water are to be used. One bar welded 
in this way is to be tested in tension; another is to be nicked to 
the depth of the weld aud beot or broken if possible to show the 
character of the welded surfaces. 

Homogeneity Test. — A portion of the test-piece is nicked 
with a chisel, or grooved ou a machine, transversely about ■^\ 
inch deep, in tliree places about 1^ inches apart. The first groove 
should be made on one side 1^ inches from the square end of the 
piece; the second, IJ inches from it on the opposite side; and the 
third, 1^ inches from the last, and on the opposite side from it. 
The test piece is then put in a vise, with the first groove about IJ 
inches above the jaw, care being taken to hold it firmly. The 
projecting end of the test-piece is then broken off by means of a 
hammer, a number of light blows being used, and the bending 
being away from the groove. The piece is broken at the other 
two grooves in the same manner. The object of this treatment is 
to open and render visible to the eye any seams due to failure to 
weld up, or to foreign interposed matter, or to cavities due to gas- 
bubbles in the ingot. 

After rupture one side of each fracture is examined, a pocket- 
lens being used, and the length of the seams and cavities is de- 
termined. The length of the longest seam or cavity determines 
the acceptance or rejection of the plate. (Any seam or cavity f 
inch long in either of the three fractures should cause rejection.) 

Quenching Test. — Steel heated to cherry -red, plunged in 
water at 82° Fahr., then bent round a curve 1| times the diameter 
of the plate, should show no signs of fracture on the outside of the 
curve. 

Steel below .10 carbon should be capable of doubling flat with- 
out fracture after being chilled from a red heat in cold water. 
Steel of .15 carbon will occasionally admit of the same treatment, 
but will usually bend around a curve whose radius is equal to 
the thickness of the specimen; about 9 percent of specimens 
stand the latter bending test without fracture. As the steel be- 
comes harder its ability to endure this bending test becomes more 
exceptional, and when the carbon ratio becomes .20 little over 
25 per cent of specimens will stand the last-described bending 
test. 

Acid Tests for Iron and Steel.— The sample to be tested is 
filed smooth on all sides, then placed in dilute nitric or sulphuric 



METALS. — STEEL. 125 

acid from 12 to 24 hours, then washed and dried. The action of 
the acid has revealed the structure of the material, from which 
its quality can be decided with great precision. 

The best steel presents a frosty appearance, ordinary steel 
honeycombed; the best iron shows the finest fibres. Should the 
iron be uneven or made from a pile of different kinds of iron all 
are exposed by the action of the acid. Hammered blooms show 
slag and iron. Gray cast iron shows crystals of graphitic carbon; 
other cast iron shows different figures, all with marked character- 
istics. 

Shop Inspection of Iron and Steel. 

The various processes in the shop are the same for both iron 
and steel, and are as follows : (1) Straightening (when necessary), 
(2) marking off and punching, (3) straightening, (4) reaming, (5) 
assembling, (6) reaming, (7) riveting, (8) facing, (9) boring, 
(10) finishing, (11) fitting up, (12) oiling and painting, (13) 
shipping. 

After the material has reached the shop the inspector wants to 
watch the work as it proceeds through the various stages to see 
that the workmanship is good and that the material is not mal- 
treated. He should have in his possession a copy of the specifi- 
cations, a bill of the material, and a set of working drawings. 

He should make a critical examination of all the dimensions of 
finished parts, location of rivet- and bolt-holes for field connec- 
tion, and have all errors corrected. 

Straightening. — The inspector should see that any of the 
material which may have been bent in transferring from the mill 
to the shop is properly straightened before being laid off for 
punching. After punching the material must be again straight- 
ened, because it is more or less buckled during the process. If 
not straightened the several pieces to be riveted together cannot 
be made to fit properly, and when riveted there will be sufficient 
spring between the pieces to distort the rivet, and many of them 
will be found to be loose on cooling. The finished member also 
never looks as well as if the material had been straightened. 

Riveting. — The punch-dies should be examined occasionally 
to see that the edges are sharp and unbroken, and that the 
difference in diameter between the upper and lower does not 
exceed -^^ inch. 

If the rivet-holes are worked with templets the templets must 
lie flat without distortion when the marking is done. 



12Q METALS.— STEEL. 

W;;ere riveting is to be done in the field the parts must oe 
fitted together in the shop and the riveVholes reamed out while 
they are assembled, or an iron templet should be made and both 
parts leamed to fit it. 

Web-splices and all abutting sections should be made to closo 
tightly and the splice-plates fitted on and reamed while in posi- 
tion. 

Drifting for any purpose other than bringing the piece to the 
proper position should not be allowed. After the work is bolted 
together and some rivets driven the use of the drift-pin is dan- 
gerous, as it is now enlarging the rivet-hole at the expense ol 
serious compression in some of the component pieces; there can 
be nothing but distortion, as the work is held by the rivets already 
driven. 

The inspector should see that a suflicient number of bolts aro 
used to hold the pieces snugly together while being riveted; also 
that all stiffeners fit tightly and that all surfaces to be riveted 
together ai e painted before being bolted up. 

As soon as the riveting is done each rivet should be examined 
to see that it is properly formed and tightly driven. (See Rivet- 
ing, page 194.) 

Facing and Boring. — In facing and boring care should be 
taken that the ends of each piece are planed to the proper length 
and bevel, and that pin-holes are of the proper size and distance 
apart from centre to centre. 

The inspector should supervise the laying out of the sections 
that are to be fitted together in the field, and see that everything 
goes together, so that no unnecessary work will have to be done 
in the field. 

After the shop- work is completed, and before painting or oiling 
is commenced, the inspector should satisfy himself that every- 
thing has been done according to the specifications and drawings; 
any part found unsatisfactory should be replaced and perfected. 
The parts found satisfactory should be marked. 

Comparing Measures. — The steel tape and other measures 
used by the inspector should be compared with the standard 
used in the shop, and corrected if necessary. 



METALS. — STEEL. 



127 



Records. — A daily record of the progress of the sb op-work 
must be kept, and especially if tbere is a time-penalty clause in 
the specifications. A record-book ruled as below will be found 
useful : 



[Left-hand pageJ] 



No. of 


Name of 


Date. 






i 


Drawing. 


Piece. 


a 

3 


> 








Ph 


Ph 


P^ 















[Bight-hand page.] 




To avoid the frequent handling of a large number of sheets of 
drawings, tables containing all of the important descriptions of 
the several pieces should be prepared in note-book form some- 
what on the following plan : 

CHORDS AND POSTS. 









a 




e8 


1 

bo 














i 

o 


< 

o 

.a 




a5 
o 


m 

O 

1 


a 

i 

o 


ma 
d 03 




1 


CO 

1 

p. 


Remarks. 


d 


a 


a 


c 


o 


o 


o 


1^ 


o 


1 




'A 


'A 


hJ 


►J 


OS 


Oi 


cc 


H 


O 


O 


m 





























128 METALS. —STEEL. 

For floor-beams and striDgers the table would be as follows : 
FLOOR-BEAMS AND STRINGERS. 













i 


















8 






Bevels. 








i 


£ 

u 


a 




















^ 


§ 


W 






Vertical. 


Horizontal. 


tb 


§ 




5 
'6 


1 


■S5- 
■0.2 










s 










1 






o 


1 


II 






-d 


a 


-d 


a 




o 




O 


^ 


W 

^ 




o 
'S . 


S 


•1. 














4-1 


1^ 




fl'O 




e"© 


o 


2 


fee 


o 


o 


o 


o 


eg 


T3 


03 a 


-d 


S s 




£ 


<D 


o 




® 


s 


(X) 


S-H 


s 


OH 


d 


ei 


S 


S 


N 


d 


N 


« 


M 


M 


^ 


^ 


J 


M 


c» 


^ 


M 


P5 


^ 


1^ 


fa 


H 



























Tables for other items, as pins, rollers, eye-bars, bracing-rods, 
lateral plates, pedestals, etc., are easily formed. 

The keeping of a complete record of the work involves consid- 
erable clerical work, which has to be done at odd times and in 
the evening. But the time and labor expended are paid for many 
times over by the sense of absolute security which the inspector 
is thereby enabled to enjoy. 

Where possible the inspector should see tnat the material is 
properly loaded on the cars for shipment in order to prevent its 
being bent or twisted in transit. He should also approve the 
itemized bill of lading of each car-load of material which he has 
accepted. 



METALS. —STEEL. 129 



Notes on Working Iron and Steel. 

Cold-rolling of iron and steel increases the elastic limit and 
the ultimate strength, but decreases the ductility. 

Punching and Shearing. — The physical effects of punching 
and shearing, as denoted by tensile tests, are for iron or steel : 
Reduction of ductility ; elevation of tensile strength at elastic 
limit ; reduction of ultimate tensile strength. 

In very thin material the disturbance described is less than in 
thick. In material having a thickness of half an inch and up- 
wards the loss of tenacity ranges from 10 to 23 per cent in iron 
plates and from 11 to 33 per cent in mild steel. 

The effects described do not invariably ensue. For unknown 
reasons there are sometimes marked deviations from what seems 
to be a general result. 

Annealing. — The object of annealing structural steel is for 
the purpose of securing homogeneity of structure that is supposed 
to be injured by unequal heating or by the manipulation attend- 
ant on certain processes. The objects to be annealed should 
be heated throughout to a uniform temperature and uniformly 
cooled. 

The temperatures employed vary from 1000° to 1500° F. and 
possibly higher. In some cases the heated steel is withdrawn at 
full temperature from the furnace and allowed to cool in the 
atmosphere; in others the heated metal is removed from the fur- 
nace, but covered under a muffle to lessen the free radiation ; or, 
again, the charge is retained in the furnace, and the whole mass 
cooled with the furnace, and more slowly than by either of the 
other methods. 

Soft steel no matter how low in carbon will harden to a 
certain extent upon being heated red-hot and plunged into water; 
it will harden more when plunged into brine and less when 
quenched in oil. 

Unannealed soft steel for a strength of 56,000 to 64,000 lbs. 
may be worked in the same way as wrought iron. Rough treat- 
ment or working at a blue heat must, however, be prohibited. 
Shearing is to be avoided except to prepare rough plates, which 
should afterwards be smoothed by machine tools or files before 
using. Drifting is to be avoided because the edges of holes are 
thereby strained beyond the yield-point. Upsetting, cranking^ 



130 METALS. — STEEL. 

and bending ought to be avoided, but when necessary the material 
should be annealed after completion. 

Forging consists in raising metal to a high temperature and 
hammering it into any form that may be required. 

In the operation of forging care must be exercised to avoid 
overheating or burning the metal. Steel requires more care than 
iron. Each variety of steel differs as to the heat to which it can 
safely be raised. 

Shear steel will stand a white heat. 

Blister steel will stand a moderate heat. 

Cast steel will stand a bright red heat. 

By overheating the tensile strength and ductility are both 
seriously injured. 

After reaching the proper heat the metal should be worked as 
quickly as possible, as working at too low a temperature is also 
injurious. 

Welding is the process by which two pieces of metal are 
joined together with the aid of heat. 

Wrought iron possesses the property of welding to a high 
degree. At a white heat it is so pasty that if two pieces at this 
temperature be firmly pressed together and freed from oxide or 
other impurity they unite intimately and firmly. 

Steel possesses the property of welding in an indifferent degree, 
which diminishes as the metal approximates to cast iron with 
respect to the proportion of carbon; or, what amounts to the 
same thing, it increases as the metal approximates to wrought 
iron with respect to the absence of carbon. 

It is usually specified that no welding shall be allowed on any 
steel that enters into structures. 

Hardening Steel. — If steel at a red heat be plunged into cold 
water it becomes hard. The more suddenly the heat is extracted 
the harder it will be. 

The process of hardening, however, makes the steel very brittle, 
and in order to make it tough enough for most purposes it has to 
be tempered. 

Tempering Steel. — The process of tempering depends upon 
the characteristic of steel, which is that if (after hardening) the 
steel be reheated, as the heat increases the hardness diminishes. 

In order to produce steel of a certain degree of toughness it is 
gi-adually reheated, and then cooled when it arrives at that tem- 
perature which experience has shown will produce the limited 
degree of hardness required. 



METALS. —STEEL. 131 

Heated steel becomes covered with a thin film of oxidation, 
which becomes thicker and changes color as the temperature 
rises. The color of this film is therefore an indication of the 
temperature of the steel upon which it appears. 

Advantage is taken by the workman of this change of color. He 
watches for the arrival of the color due to the required tempera- 
ture. When it appears he withdraws the tool from the fire and 
plunges it into cold water and moves it about until the heat has 
all been extracted by the w^ater. 

It is important that considerable motion should be given to the 
surface of the water while the tool is plunged in; otherwise there 
will be a straight line of demarcation between the hardened part 
and the remainder of the tool, and the metal will be liable to 
snap at this point. 

Upsetting. — Enlarged ends on tension-bars for screw- threads, 
eye-bars, etc., are formed by upsetting the material. With 
proper treatment and a sufficient increment of enlarged sectional 
area over the body of the bar the result is entirely satisfactory. 

The upsetting process should be performed so that the properly 
heated metal is compelled to flow w^ithout folding or bending. 

Calking. — All calkin g-edges should be bevelled on a planer, 
and the calking should be done with a round-nosed tool. If a 
square-edged tool is used it creases the inner plate, and if this 
should prove to be of brittle steel it might cause a failure along 
this line. 

Blue-shortness. — Steel and wrought iron are injured and 
rendered brittle by being worked at a blue heat, i. e., the heat that 
would produce an oxide coating ranging frv)m light straw to blue 
on bright steel (430° to 600° F.). 

A practice among boilermakers for guarding against faihires 
due to working at a blue heat consists in the cessation of work as 
soon as a plate which had been red-hot becomes so cool that Uie 
mark produced by rubbing a hammer-handle or other piece of 
wood will not glow. A plate which is not hot enough to produce 
this effect, yet too hot to be touched by the hand, is most prob- 
ably blue-hot, and should under no circumstances be hammered 
or bent. 



131^ METALS. — STEEL. 



Standard Specifications for Special Open-hearth 
Plate, Structural, Pin and Rivet Steel, and 
Structural Cast Iron. 

[Adopted by the Ass'n Am. Steel Manufacturers July 17, 1896.1 

Special Open-hearth Plate Steel. — Steel shall be of four 
grades — extra soft, fire box, flange or boiler, and boiler rivet 
steel. 

Extra Soft Steel. — Ultimate strength, 45,000 to 55,000 pounds 
per square inch. Elastic limit, not less than one half the ulti- 
mate strength. Elongation, 28 per cent. Cold and Quench 
bends, 180° flat on itself, without fracture on outside of bent 
portion. Maximum phosphorus, .04 per cent ; maximum sul- 
phur, . 04 per cent. 

Fire-box ^^^6^.— Ultimate strength, 52,000 to 62,000 pounds 
per square inch. Elastic limit, not less than one half the ulti- 
mate strength. Elongation, 26 per cent. Cold and Quench 
bends 180° flat on itself, without fracture on outside of bent 
portion. Maximum phosphorus, .04 per cent ; maximum sul- 
phur, .04 per cent. 

Flange or Boiler >S^6^.— Ultimate strength, 52,000 to 62,000 
pounds per square inch. Elastic limit, not less than one half 
the ultimate strength. Elongation, 25 per cent. Cold and 
Quench bends, 180° flat on itself, without fracture on outside of 
bent portion. Maximum phosphorus, .06 per cent ; maximum 
sulphur, .04 per cent. 

Boiler-rivet Steel. — Steel for boiler rivets shall be made the 
same as extra soft steel specified above. 

Test Pieces. — All tests and inspections shall be made at place 
of manufacture prior to shipment. 

The tensile strength, limit of elasticity and ductility shall be 
determined from a standard test piece cut from the finished 
material. The standard shape of the test piece for sheared 
plates shall be as shown on page 131c. On tests cut from other 
material the test piece may be either the same as for plates, or 
it may be planed or turned parallel throughout its entire 
length. The elongation shall be measured on an original length 
of eight inches, except when the thickness of the finished ma- 
terial is -f\ inch or less, in which case the elongation shall be 
measured in a length equal to sixteen times the thickness ; and 



METALS. — STEEL. 13lb 

except in rounds of | inch or less in diameter, in which case the 
elongation shall be measured in a length equal to eight times 
the diameter of section tested. Four test pieces shall be taken 
from each melt of finished material : two for tension and two for 
bending. 

Material which is to be used without annealing or further 
treatment is to be tested in the condition in which it comes from 
the rolls. When material is to be annealed or otherwise treated 
before use, the specimen representing such material is to be 
similarly treated before testing. 

Every finished piece of steel shall be stamped with the melt 
number. Eivet steel may be shipped in bundles securely wired 
together, with the melt number on a metal tag attached. 

All plates shall be free from surface defects and have a work- 
manlike finish. 

Variation when Ordered to Gauge. — For all plates ordered to 
gauge, there will be permitted an average excess of weight over 
that corresponding to the dimensions on the order equal in 
amount to that specified in the table shown on page ISle, provided 
no plate shall be rejected for light gauge measuring .01 inch 
or less below the ordered thickness. 

Variation when Ordered to Weight.— Flsites 12^^ pounds or 
heavier, when ordered to weight, shall not average more varia- 
tion than 2| per cent, either above or below the theoretical 
weight. 

Plates from 10 to 12^ pounds, when ordered to weight, shall 
not average a greater variation than the following : Up to 75 
inches wide, 2^ per cent either above or below the theoretical 
weight ; 75 inches and over, 5 per cent either above or below the 
theoretical weight. 

Structural Steel. — Steel may be made by either the open- 
hearth or Bessemer process, and shall be of three grades — rivet, 
soft, and medium. 

Bivei Steel. — Ultimate strength, 48,000 to 58,000 pounds per 
square inch. Elastic limit, not less than one half the ultimate 
strength. Elongation, 26 per cent. Bending test, 180° flat on 
itself, without fracture on outside of bent portion. 

Soft aS/^^^.— Ultimate strength, 52,000 to 62,000 pounds per 
square inch. Elastic limit, not less than one half the ultimate 
strength. Elongation, 25 per cent. Bending test, 180^ flat on 
itself, without fracture on outside of bent portion. 



131c 



META.LS. — STEEL. 



Medium Steel. — Ultimate strength, 60,000 to 70,000 pounds per 
square inch. Elastic limit, not less than one half the ultimate 
strength. Elongation, 22 per cent. Bending test, 180° to a 
diameter equal to thickness of piece tested, without fracture on 
outside of bent portion. 

Test Pieces. — All tests and inspections shall be made at place 
of manufacture prior to shipment. 

The tensile strength, limit of elasticity, and ductility shall be 
determined from a standard test piece cut from the finished 
material. The standard shape of the test piece for sheared 
plates shall be as shown by the following sketch : 



Abont 3' 



.<f 



not less than 9 ' 



^ 



1>6 



-^ 1 ) j *l% E tc.— 

-AboutlS^ 



Ab<uti2* 



Pieces to be of the same thickness as the plate. 



On tests cut from other material the test piece may be either 
the same as for plates, or it may be planed or turned parallel 
throughout its entire length. The elongation shall be measured 
on an original length of 8 inches, except when the thickness of 
the finished material is ^^ inch or less, in which case the elonga- 
tion shall be measured in a length equal to sixteen times the 
thickness ; and except in rounds of f inch or less in diameter, in 
which case the elongation shall be measured in a length equal 
to eight times the diameter of section tested. Two test pieces 
shall be taken from each melt or blow of finished material, one 
for tension and one for bending. 

Material which is to be used without annealing or further 
treatment is to be tested in the condition in which it comes from 
the rolls. When material is to be annealed or otherwise treated 
before use, the specimen representing such material is to be simi- 
larly treated before testing. 

Every finished piece of steel shall be stamped with the blow 
or melt number, and steel for pins shall have the blow or melt 
nuni])er stamped on the ends. Rivet and lacing steel, and small 
pieces for pin-plates and stiffeners, may be shipped in bundles 



METALS. — STEEL. 131^ 

securely wired together, with the blow or melt number on a 
metal tag attached. 

Finished bars must be free from injurious seams, flaws or 
cracks, and have a workmanlike finish. 

Chemical Properties. — Steel for railway bridges, maximum 
phosphorus, .08 per cent. Steel for buildings, train sheds, 
highway bridges, and similar structures, maximum phosphorus, 
.10 per cent. 

Pin Steel. — Pins made from either of the above-mentioned 
grades of steel shall, on specimen test pieces cut at a depth 
of 1 inch from surface of finished material, fill the physical 
requirements of the grade of steel from which they are rolled, 
for ultimate strength, elastic limit, and bending, but the required 
elongation shall be decreased 5 per cent. 

Eye-bar Steel. — Eye-bar material, 1| inches and less in 
thickness, made of either of the above-mentioned grades of steel, 
shall, on test pieces cut from finished material, fill the require- 
ments of the grade of steel from which it is rolled. For thick- 
nesses greater than 1^ inches, there will be allowed a reduction 
in the percentage of elongation of 1 per cent for each i of an 
inch increase of thickness, to a minimum of 20 per cent for 
medium steel and 22 per cent for soft steel. 

Full-size Test of Steel Eye-hars.-~Y\x\\-ii\ze test of steel eye-bars 
shall be required to show not less than 10 per cent elongation in 
the body of the bar, and tensile strength not more than 5000 
pounds below the minimum tensile strength required in speci- 
men tests of the grade of steel from which they are rolled. The 
bars will be required to break in the body, but should a bar 
break in the head, but develop 10 per cent elongation and the 
ultimate strength specified, it shall not be cause for rejection, 
provided not more than one third of the total number of bars 
tested break in the head ; otherwise, the entire lot will be 
rejected. 

Variation in Weight. — The variation in cross-section or 
weight of more than 2| per cent from that specified will be 
sufiicient cause for rejection, except in the case of sheared plates, 
which will be covered by the following permissible variations : 

Plates 12^ pounds or heavier, when ordered to weight, shall 
not average more variation than 21 per cent either above or 
below the theoretical weight. 



131^ 



METALS. 



-STEEL. 



Plates from 10 to 12| pounds, when ordered to weight, shall 
not average a greater variation than the following : 

Up to 75 inches wide, 2^ per cent either above or below the 
theoretical weight. 

Seventy-five inches and over, 5 per cent either above or below 
the theoretical weight. 

For all plates ordered to gauge there will be permitted an 
average excess of weight over that corresponding to the dimen- 
sions on the order equal in amount to that specified in the fol- 
lowing table : 

ALLOWANCES FOR OVERWEIGHT FOR RECTANGULAR STEEL 
PLATES WHEN ORDERED TO GAUGE. 

ADOPTED BY THE ASS'N AMERICAN STEEL MANUFACTURERS JULY 17, 1896. 

The weight of 1 cubic inch of rolled steel is assumed to be 
.2833 lb. 







Width of Plate. 


Thickness of Plate. 


Up to 
50 in. 


50 in. 

and 

above. 


Up to 
75 in. 


75 in. 

to 
100 in. 


Over 
100 in. 


1/8 up to 5/32 in 
5/32 " 3/16 ' 
3/16 '* 1/4 * 

1/4 ' 
5/16 ' 
3/8 * 
7/16 ' 


eh 


Per cent. 
10 


Per cent. 
15 

10 


Per cent. 
10 

8 
7 
6 
5 

4 


Per cent. 

14 
12 
10 

8 

7 

6i 

6 

5 


Per cent. 
18 






16 






13 






10 


1/2 ' 
9/16 • 
5/8 ' 
over 5/8 







9 

8i 






8' 






6i 











Structural Cast Iron. — Except where chilled iron is speci- 
fied, all castings shall be tough gray iron, free from injurious 
cold -shuts or blow-holes, true to pattern, and of a workmanlike 
finish. Sam] la pieces, one inch square, cast from the same 
heat of metal in sand moulds, shall be capable of sustaining on 
a clear span of 4 feet 8 inches, a central load of 500 pounds when 
tested in the rough bar. 



132 METALS. — COPPER. • 

Copper. 

Copper is obtained from the ores by roasting, calcining, refin- 
ing, and melting them with certain fluxes and oxidizing agents. 

It is distinguished from all other metals b}^ its reddish color. 

It is veiy ductile and malleable and its tenacity is next to iron. 

It cannot be welded. It may be worked either hot or cold. 

It oxidizes very slowly in the air, becoming coated with a thin 
film of the carbonate called verdigris; this protects it from further 
oxidation. 

It is corroded by salt water if at the same time air has access to it. 

Copper is used for slate-nails, pipes, roofing-gutters, lightning- 
rods, and in the form of sheets, bars, and wire is extensively used 
in electrical work and for many other purposes. 

Properties of Copper. 
Specific gravity 8.81 to 8.95 

Weight per cubic foot \ ^^^^' ^^^ ^^«- 

( Sheet, 555 " 

Melting-point 1930° F. 

Atomic weight 63.2 

Specific heat 093 

Conductivity of heat : 73.6 

** •* electricity 99.95 (silver 

being 100) 

Expansion between 32° and 212° F 0051 

Resistance to tension, 20,000 to 33,000 lbs. per square inch, being 

reduced at a temperature of 400° F. 10 per cent, and at 500' 

F. 16 per cent. 

Resistance to crushing 117,000 lbs. per square inch 

Tests for Copper. — Copper in the form of plates, sheets, or 
bars is subjected to a tension test and to a bending test both hot 
and cold. Copper wire is subjected to tension, bending, and 
winding or torsional tests. 

Table 15. 
WEIGHT OF round BOLT COPPER. 
Diameter. ^^^^^^ 

^°^"®^- Pounds. 

f 425 

i 756 



i 1.18 

f 1.70 

I 2.31 

1 3.02 

U 3.83 



Diameter. ^r^f^^ 

Inches ^^^ ^*^^'' 

^^^^^^' Pounds. 

1\ 4.72 

If 5.72 

U 6.81 

If 7.99 

If 9.27 

1| 10.64 

2 12.10 



METALSo— COPPER. 



133 



Table 16. 

COPPER AND BRASS. GAUGE AND WEIGHT OF WIRE AND SHEET. 







Weight of Wire per 


Weight of Plates per 


No. of 
Gauge. 


Size of 
Each No. 


1000 Lineal Feet. 


Square Foot. 














Copper. 


Brass. 


Copper. 


Brass. 




Inch. 


Pounds. 


Pounds. 


Pounds. 


Pounds. 


0000 


.46000 


640.5 


605.28 


20.84 


19.69 


000 


.40964 


508.0 


479.91 


18.55 


17.53 


00 


.36480 


402.0 


380.77 


16.52 


15.61 





.32476 


319.5 


301.82 


14.72 


13.90 


1 


.28930 


253.3 


239.45 


13.10 


12.38 


2 


.25763 


200.9 


189.82 


11.67 


11.03 


3 


.22942 


159.3 


1.50.52 


10.39 


9.82 


4 


.20431 


126.4 


119.48 


9.25 


8.74 


5 


.18194 


100.2 


94.67 


8.24 


7.79 


6 


.16202 


79.46 


75.08 


7.34 


6.93 


7 


.14428 


63.01 


59.55 


6.54 


6.18 


8 


.12849 


49.98 


47.22 


5.82 


5.50 


9 


.11443 


39.64 


37.44 


5.18 


4.90 


10 


.10189 


31.43 


29.69 


4.62 


4.36 


11 


.090742 


24.92 


23.55 


4.11 


3.88 


12 


.080808 


19.77 


18.68 


3.66 


3.46 


13 


.071961 


15.65 


14.81 


3.26 


3.08 


14 


.064084 


12.44 


11.75 


2.90 


2.74 


15 


.057068 


9.86 


9.32 


2.59 


2.44 


16 


.050820 


7.82 


7.59 


2.30 


2.18 


17 


.045257 


6.20 


5.86 


2.05 


1.94 


18 


.040303 


4.92 


4.65 


1.83 


1.72 


19 


.035890 


3.90 


3.68 


1.63 


1.54 


20 


.031961 


3.09 


2.92 


1.45 


1.37 


21 


.028462 


2.45 


2.317 


1.29 


1.22 


22 


.025347 


1.94 


1.838 


1.15 


1.08 


23 


.022571 


1.54 


1.457 


1.02 


.966 


24 


.020100 


1.22 


1.155 


.911 


.860 


25 


.017900 


.699 


.916 


.811 


.708 


26 


.014940 


.769 


.727 


.722 


.682 


27 


.014195 


.610 


.576 


.643 


.608 


28 


.012641 


.484 


.457 


.573 


.541 


29 


.011257 


.383 


.362 


.510 


.482 


30 


.010025 


.304 


.287 


.454 


.429 


31 


.008928 


.241 


.228 


.404 


.382 


32 


.007950 


.191 


.181 


.360 


.340 


33 


.007080 


.152 


.143 


.321 


.303 


34 


.006304 


.1^0 

.096 


.114 


.286 


.270 


35 


.005614 


.0915 


.254 


.240 


36 


.OC5000 


.0757 


.0715 


.226 


.214 


37 


.004453 


.0600 


.0567 


.202 


.191 


38 


.003965 


.0476 


.0450 


.180 


.170 


39 


.003531 


.0375 


.0357 


.160 


.151 


40 


.003144 


.0299 


• .0283 


.142 


.135 


Specific gravi 
Weight per ci 


ty 


8.880 


8.386 


8.698 


8.218 


abicfoot...... 


555. 


524.16 


543.6 


513.6 



134 METALS.— LEAD. 



Lead. 

Lead is obtained by smelting the various lead ores, and as 
a by-product in the smelting of silver ores. It is soft, heavy, 
malleable, and ductile, but its tenacity is such that it can be 
drawn into wire with great difficulty. Is very fusible; melts at 
about 625° F., softens and becomes pasty at about 617° F. If 
broken by a sudden blow when just below the melting-point it 
is quite brittle and the fracture appears crystalline. It dissolves 
to some extent in pure water, but water containing carbonates or 
sulphates forms over it a film of insoluble salt which prevents 
further action. Lead is oxidized by rain-water, vegetable matter, 
lime, damp plaster, and wet wood; also by galvanic action when 
in contact with other metals in the presence of moisture. It is 
also rapidly destroyed by ammonia, acetates, nitrites, and nitrates 
in solution. It does not readily decompose on exposure to the 
atmosphere, being usually protected by the first coat of oxide 
which forms upon its surface. 

The white lead of commerce is formed from the carbonate of 
lead. Red lead is a compound oxide of lead. 

Properties of Lead. 

Specific gravity 11.07 to 11.44 

Weight per cubic foot {£tj?y''- 

Melting-point 625" F. 

Atomic weight 206.4 

Specific heat .0314 

Conductivity of heat 8.5 

'* *' electricity (silver i)eing 100). ... 8.3 

Expansion between 32° and 212° F .0084 

Resistance to tension 1600 to 2400 lbs. per sq. in. 

Resistance to compression 7730 lbs. per sq. in. 

Sheet Lead is either cast or milled, the former in sheets 16 to 
18 feet in length and 6 feet in width ; the latter is rolled, is thinner 
than the former, is more uniform in its thickness, and is made into 
sheets 25 to 35 feet in length, and from 6 to 7i feet in width. 

Sheet lead is usually described according to the weight of a 
superficial foot in pounds. The thicknesses corresponding to given 
weights are as follows : 



METALS. — LEAD. 



135 



Table 17. 

THICKNESS AND WEIGHT OF SHEET LEAD. 



Weight per 

Square Foot. 

Lbs. 



Thickness. 
Inches. 

1 0.017 

2 0.034 

3 0.051 

4 0.068 

5 0.085 

6 0.101 

7 0.118 



Weight per 

Square Foot. 

Lbs. 



Thickness. 
Inches. 

8 0.135 

9 0.152 

10 0.169 

11 0.186 

12 0.203 

14 0.237 

16 0.271 



Sheet lead is used in roofing for gutters, flashings, etc. ; for 
lining cisterns, sinks, etc. The weights recommended for these 
purposes are as follows : 

Roofs and gutters 7 lb. lead 

Hips, ridges, and small gutters 6 *' * * 

Flashings 4 and 5 ** " 

Cisterns and sink bottoms 7 ** *' 

'* '* sides 6 ** '' 

Owing to the great expansion and contraction of lead from al- 
terations of temperature it is not desirable to lay it in greater 
iicngths than 10 or 12 feet without a joint roll or drip to allow for 
the changes in dimensions. 

Lead Pipes are formed by drawing, casting, pressing, or roll- 
ing lead. They are usually described by the diameter and 
weight per foot, as shown in Table 65. 



136 METALS.— TIN. 



Tin. 

Tin is obtained by roasting and smelting the ores— usually the 
binoxide and tin pyrites — in a reverberatory furnace, whence the 
liquid metal is run into a basin and thence into moulds. The 
ingots thus produced are refined and boiled. 

Tin is a soft, malleable, fusible, white, lustrous metal of little 
strength. It resists oxidation better than any of the metals 
except gold and silver. Its chief uses are for coating sheet iron, 
called "tin plate," and for making alloys with copper and other 
metals. 

Tin may be distinguished from other metals by the peculiar 
crackling sound (termed the " cry of tin") produced when bent. 
Its purity is tested by its extreme brittleness at high tempera- 
tures. 

Tin in pigs or plate is subject to a peculiar foim of disaggre- 
gation, especially when exposed to extreme cold and great 
changes of temperature. Thin sheet tin will sometimes, if ex- 
posed to the cold for loug periods, be covered with blisters, 
become brittle, fall to pieces, and finally to powder. The cause 
of the deoay of tin has not been definitely settled, but the pres- 
ence of mercury seems to aid it. 

Properties of Tin. 

Specific gravity 7.293 

Weight per cubic foot, cast 456 lbs. 

Melting-point 442° F. 

Atomic weight 118 

Specific heat 055 

Conductivity of heat 14.5 

" '* electricity (silver being 100) 12.4 

Expansion between 32° and 212° F c 00C9 

Resistance to tension 3500 lbs. per sq. in. 

Resistance to compression 15,500 lbs. per sq. in. 

Tin Plate is iron or steel plate covered with a coating of tin 
or an alloy of tin and lead. 

Tin plate is extensively used for roofing, leader-pipes, flashing, 
and other purposes. Such plates are durable until a hole is made 
in the coating, when galvanic action sets up between the tin and 
iron; the tin is Iheu rapidly eaten away. 



METALS.— TIN. 137 

Tin plate is made of sheet iron or steel coated with tin or a 
mixture of tin and lead. Plates of the first class are designated 
"bright tin" plate, and of the latter class ''terne'' (dull) plate. 
Very thin sheets which run be'ow gauge (30 or lighter) are called 
*' taggers" tin. Imperfect plates are called '' wasters." 

The plates are coated by various processes: 1. The Dipping 
Process^ in which the plates, prepared by pickling in dilute 
sulphuric acid, annealing, and again pickling, are dipped in a 
bath of palm-oil, then in a bath of molten tin, from which they 
go to the rollers. *' Redipped " plates are plates dipped a second 
time in the molten tin. Acid Process: In this process the 
cleaned and pickled plates are passed through a solution of muri- 
atic acid and zinc chloride which floats on top of the molten tin. 
The zinc causes a quick galvanic action, and as the plates are 
immersed in the molten tin the tin by means of this galvanic 
action will adhere to the plates. The plates thus tinned are 
drawn through an oil bath. Plates prepared by this process are 
not as durable as those coated by the palm-oil process. Boiler 
Process: In this process the plates are dipped in the molten 
metal, and then passed through rolls which work in a large vessel 
containing oil. The rolls are adjusted so as to leave a coating of 
greater or less thickness, which determines the value of the plate. 

Two thicknesses of tin roofing- plates are made, namely, IC, or 
No. 29 gauge, weighing 8 oz. to the square foot, and IX, or No. 
27 gauge, weighing 10 oz. to the square foot. 

The sizes of plates generally used for roofing are 14 X 20 and 
20 X 28 in. The larger size is more extensively used, because it 
requires less seams and consequently cheapens the cost of putting 
on; but a better roof is obtained by using 14!' X 20'', because the 
seams are closer together, thus making the roof stronger; and if 
put on with a standing seam there is more allowance for expan- 
sion and contraction. 

The value of tin roofing-plate is dependent upon five things: 
1st. The quality of the material of which the plate is made. 

The best plates for tinning are of charcoal-iron, which, being 
tough, bears bending. Coke-iron is used for cheaper plates. It 
is inferior as regards bending. Open -hearth and Bessemer steel 
plates are now generally used in place of iron. The former 
is used for the better grades, the latter for inferior grades. 

2d. The coating, whether it is tin or a mixture of tin and lead; 
the latter is not so durable as the former. The thickness of tha 
coating; this can be determined by trying with a knife. 



138 METALS.— TIN. 

3d. The net weight of the hundred and twelve sheets in the 
box. The standard weight of an ordinary IC 14 X 20 inch plate 
is 108 pounds to the 112 sheets, but there are many boxes im- 
ported that run all the way from 90 to 120 pounds in weight. 
The standard weight of a box of IX 14" X 20" is 136 pounds, and 
of IX 20" X 28", 272 pounds. There are IX 14 X 20 plates im 
ported that do not weigh over 120 pounds per box, while others 
weigh as much as 150 pounds for the same size. It may be that 
the lighter sheets have as heavy a coating of lead and tin as the 
heavier sheets, but the possibility is that they have not. The 
quantity of tin required for coating 112 sheets of 14" X 20" IC 
plate is 3J lbs., but as low as 21 lbs. are said to De used. The 
amount of tin used in coating the plates is very irregular; a few 
years ago 7 lbs. to the box was considered the average, but now 
as little as 2 lbs. per 100 lbs. of iron is used. 

4th. The squareness of the sheets. 

5th. The assortment of the sheets. In the manufacture of tin 
plates there occur imperfect sheets, having corners and edges 
broken, spots not covered with tin, etc. These are packed by 
themselves in separate boxes, and denominated as ''wasters," 
while tlie perfect sheets are denominated '* prime" plates. The 
boxes containing "wasters'* or imperfect sheets are marked 
"ICW" or "IXW," according to the thickness; so that where 
the letter " W" appears on a box it shows that the box contains 
imperfect sheets, and should not be accepted when ** prime " tin 
is specified. 

It is now becoming the custom to stamp every sheet with the 
name of the brand and thickness before leaving the factory. 



METALS. — TIN. 



139 



Table 18. 

TIN PLATES (TINNED SHEET STEEL). 



BRAND. 



IC IX IXX 



IC IX IXX IXXX IXXXX IX IXX 



THICKNESS, B. W. GAUGE. 



29 


27 


26 




29 


27 


26 


25 


24i 


27 



26 



NUMBER OF SHEETS PER BOX. 



h 


225 


225 




112 


112 


112 112 112 


56 











NET WEIGHT PER BOX. 








Size, 
Indies. 


Pounds. 


Size. 
Inches. 


Pounds. 


IC X 14 


108 


135 


160 


14 X 20 


108 


135 


160 


180 


200 






12 X 12 


110 
132 


138 
162 


165 
192 


20 X 28 
18 X 18 


216 
138 


270 

158 


320 

178 






180 




13 X 13 








14 X 14 


155 


193 


230 


20 X 20 


160 


195 


222 










15 X 15 


178 


218 


260 


22 X 22 


190 


235 


275 










16 X 16 


200 


248 


290 


24 X 24 


220 


276 


330 










17 X 17 


280 


289 


340 


12 X 24 


110 


138 


165 










10 X 20 


160 


195 


222 


13 X 26 


132 


162 


192 










11 X 22 


190 


235 


275 


14 X 22 
14 X 24 
14 X 28 
14 X 56 


120 
130 
155 


148 
161 
193 


174 
190 
230 






185 


220 










14 X 31 


178 


210 


240 


















14 X 60 

15 X 21 


120 


152 


i76 






200 


240 


















16 X 19 


120 


147 


170 


















16 X 20 


127 


154 


180 


















16 X 22 


138 


170 


200 











BRAND. 



DC 



DX 



DXX 



DXXX 



DXXXX 



THICKNESS, B. W. GAUGE. 



28 



25 



24 



23 



22 



NUMBER OF SHEETS PER BOX- 



100 



100 



100 



100 



100 





NET WEIGHT 


PER BOX. 






Size. Inches. 


Pounds. 


12J X 17 
15 X 21 


94 
130 


122 

180 


143 
213 


164 
244 


185 
275 



NUMBER OF SHEETS PER BOX. 



17 X 25 



5 

94 iosT 



."0 
122 llKs. 



.')0 
14::5 ih^ 



Mil ll)s. 



_50 

185 lbs. 



140 



METALS. — TIK. 



Terne plates, 
112 sheets per box 



10'' X 20'' IC, 80 lbs.; IX, 100 lbs. 
14 X 20 IC, 112 '* IX, 140 " 
20 X 28 IC, 224 ♦* IX, 280 '* 



Taggers tiu and iron, ) ia v 14 and 14 X 20 112 lbs ner box 

The a ea of roof covered by any sheet is less by 2 inches in 
width and 1 inch in length than the proposed sheet. 



Table 19. 

WEIGHT OF SHEETS OF WROUGHT IRON AND STEEL. 
WEIGHTS PER SQUARE FOOT. THICKNESS, BIRMINGHAM GAUGE. 



No. 


Thick- 






No. 


Thick- 






of 


ness. 


Iron. 


Steel. 


of 


ness. 


Iron. 


Steel. 


Gauge. 


Inches. 






Gauge. 


Inches. 






0000 


.454 


18.22 


18.46 


16 


.065 


2.61 


2.64 


000 


.425 


17.05 


17.28 


17 


.058 


2.33 


2.36 


00 


.38 


15.25 


15.45 


18 


.049 


1.97 


1.99 





.34 


13.64 


13.82 


19 


.042 


1.69 


1.71 










20 


.035 


1.40 


1.42 










21 


.032 


1.28 


1.30 


1 


.3 


12.04 


12.20 


22 


.028 


1.12 


1.14 


2 


.284 


11.40 


11.55 


23 


.025 


1.00 


1.02 


3 


.259 


10.39 


10.53 


24 


.022 


.883 


.895 


4 


.238 


9.55 


9.68 


25 


.02 


.803 


.813 


5 


.22 


8.83 


8.95 


















26 


.018 


.722 


.732 










27 


.016 


.642 


.651 










28 


.014 


.562 


.569 


6 


.203 


8.15 


8.25 


29 


.013 


.522 


.529 


7 


.18 


7.22 


7.32 


30 


.012 


.482 


.488 


8 


.165 


6.62 


6.71 










9 


.148 


5.94 


6.02 


31 


01 


.401 


.407 


10 


.134 


5 38 


5.45 


32 


.009 


.361 


.366 










33 


.008 


.321 


.325 










34 


.007 


.281 


.285 


11 


.12 


4.82 
4.37 


4.88 
4.43 


35 


.005 


.201 


.203 


12 


.109 










13 


.095 


3.81 


3.86 


Sp. gr 




7.704 


7.806 


14 


.083 


3.33 


3 37 


Wt. CL 


I.* ft..". 


481.25 


487.75 


15 


.07:i 


2.89 


2.93 


I 


Id. . . 


.2787 


.'.:8;.^3 



METALS. — ZIKC. 141 



Zinc. 



Zinc is obtained from the carbonate, sulphide, and red oxide 
ores. The ore is roasted, mixed with charcoal, and heated in 
retorts. The zinc is converted into vapor, which is condensed 
and subsequently fused. 

Zinc is a rather hard, bluish-white metal, tough and not easily 
broken by blows of the hammer at ordinary temperatures, but 
when heated to a point approaching that of fusion it becomes brit- 
tle. At temperatures between 210'' and 300° F. it is ductile and 
malleable, and may be rolled into sheets, and drawn into moder- 
ately fii^e wire, which, however, possesses but little tenacity. 

Pbopekties of Zinc. 

Specific gravity 7.14 

Weight per cubic foot, cast. 428 lbs. 

Melting-point, 780° F. ; volatilizes and burns in the air 
when melted with bluish-white fumes of zinc oxide. 

Atomic weight 65 

Specific heat 096 

Conductivity of heat 36 

** '* electricit}'' 29 (silver being 100) 

Tenacity 5000 to 6000 lbs. per. sq. in. 

Expansion between 32° and 212° F 0.0088 

Zinc is used for making brass and other alloys, and for coating 
iron surfaces, called *' galvanizing." 

For the purpose of galvanizing the iron is dipped into dilute 
sulphuric acid to remove scale, etc., and then plunged into a bath 
of molten zinc covered with sal-ammoniac. 

Combined with copper it forms brass, and with the addition of 
tin and other metals various similar alloys are formed, which are 
distinguished by specific names. 

Zinc forms the base of the zinc paints. 

Zinc should not be used in contact with copper, iron, or lead, 
as voltaic action is set up, especially when moisture is present, 
thus destroying the zinc. Soot, lime, water containing lime, and 
acid woods, such as oak, are also very destructive of it. When 
first exposed to the action of the atmosphere it is speedily cor- 
roded, but the film of caibouate of zinc thus formed protects it 
from further oxidation. 



142 METALS. — ALUMINUM. 

Good sheet zinc is of a uniform color, tough and easily bent 
backwards and forwards without cracking. 

Inferior zinc is of a darker color than the pure metal and of a 
blotchy appearance caused by the presence of other metals, which 
set up a galvanic action and soon destroy the zinc. 

Aliiniinuin, 

Aluminum is a white, soft, malleable metal of extreme light- 
ness, its specific gravity being only 2.56 when cast and 2.75 when 
rolled. It melts at about 1150" F., but does not volatilize at 
ordinary melting temperatures. It is especially free from oxida- 
tion and corrosion in air, as neither oxygen, carbonic acid, car- 
bonic oxide, sulphuric or nitric acid, sea-water, nor sulphuretted 
hydrogen has much effect on it. It is, however, readily dissolved 
by hydrochloric acid and by caustic alkalies. Its strength pure, 
when cast, is only about 18,000 ])ounds per square inch, with 
low elastic limits in tension and compression. When rolled or 
drawn into wire its strength is raised to from 25,000 to 50,000 
pounds per squaretinch, with elastic limits of about one half the 
ultimate strength. It is seldom used in a pure state because of 
its softness, but makes with copper, iron, zinc, and tin remarka- 
bly strong and malleable alloys. 

Aluminum may be rolled either hot or cold. It is annealed 
by bringing it to a low red heat and cooling slowly. In casting 
aluminum care must be taken to provide for the great shrink- 
age. It is best to cast in hot iron moulds and to cool from the 
bottom artificially, keeping melted metal at the gate to supply 
the shrinkage. Casting under pressure also gives good results. 

It is difficult to obtain aluminum in a perfectly pure state, 
J nd very slight amounts of impurities affect its properties. 
The common impurities are iron and silicon. 

Aluminum is largely used in the manufacture of steel, the 
amount used, however, being comparatively small (from 2 to 5 
ounces to the ton of steel), varying with the grade of steel being 
made. It is added to the heat just before drawing or teeming, 
or in the ladle after drawing. Its use prevents the formation and 
c: cape of gases, improves the homogeneity of the steel, gives 
s(<lid ingots or castings ; it quiets the ebullition in molten steel, 
thereby allowing the successful pouring of "wild" heats from 
the furnace ; it prevents blow-holes and adds to the ductility of 
JiC product. 



METALS. —ALLOYS. 142a 

Alloys. 

The term alloy is generally applied to all combinations ob- 
tained by fusing metals with each other, except when mercury 
is one of the combining metals, in which case the compound is 
called amalgam. Many of the alloys are importantly useful, as 
brass, bronze, etc. 

The specific gravity of alloys does not follow the ratio of that 
of their components; it is sometimes greater and sometimes less 
than the mean, showing that in some cases expansion has taken 
place, and in others contraction. 

Brass is an alloy of copper and zinc, in proportions varying 
with the purpose for which the metal is required. The color is 
dependent upon the proportions. It is rendered brittle by contin- 
ued impacts, is more malleable than copper when cold, is imprac- 
ticable of being forged, as its zinc melts at a low temperature. 
Its malleability is decreased as the proportion of zinc is increased. 
Its tenacity is impaired by the addition of lead or tin. Its fusi- 
bility is governed by the proportion of zinc. 

Bronze is a mixture of copper and tin, the proportions being 
varied for different purposes. Large castings in bronze are often 
not homogeneous throughout their mass in consequence of the 
difference in fusibility of the copper and tin. 

Aluminum Bronze is composed of from 90 to 95 per cent of 
copper and 10 to 5 per cent of aluminum. 

Phosphor Bronze is any bronze or brass alloy with a small 
proportion of phosphorus. 

Manganese Bronze is an alloy of pure copper with from 2 to 
30 per cent of manganese. Its color is usually white. 



Table 20. 

ALLOYS AND COMPOSITIONS. 



143 



* 


Cu 


Zn 


Sii 


Ni 


Pb , Sb 


Bi 


Al 


Argentan 


.^5 
95 

3.7 
84.3 
75 

79.3 
92.2 
90 
80 

88.8 
74.3 
50 
88.9 
90 
10 

3 

67 
66 

87" 

86 

67.2 

90 

93 

95 

80 

93 

92 

90 

91.4 

16 

58.1 

40.4 

80 

69 

87 5 

72 

33.3 

40.4 

49.5 

81.6 

90 

77 

80 

87.5 

77.4 

60 

56" 

66 

50 

86 

66.6 

33.4 

'7A 
69.8 

73 


24 

'5^2 
25 
6.4 
.... 

20 
11.2 
22.3 
31 

2.8 

80'" 
90 

33' 
34 

i3* 
11.1 
31.2 

5^5 

1 

17.2 
25.4 

5.6 

33; 4 
25.4 
24 

3*' 

'7" 

40 

45* 

21" 
4 

'7;4 

25.8 

12.3 


89" 
10.5 

i4'.3 

7.8 
9 

'3.4 

*8'.3 

10 

10 

25" 

'2'.9 
1.6 
10 

7 

5 
20 
. 7 

8 
10 

1.4 

1 

*2!6 

10.1 

31 

12.5 

26.5 

is.'i 

9 
23 
20 
12.5 
15.6 

86* 
80 

22*' 

29 

6 

33.4 
66.6 

28^4 

4.4 

(Mas 

1Sal- 


21 
19" 

lile 

31.6 

33.3 

31.6 
24 

nesia. 
am'ni£ 


46' 

'i'.7 

1 
■4:3 

75 
26" 

'4 " 

75" 

87.5 

....4.4 
IC..2.5 


'7;3 

'7" 

47 


25" 

> 
2 

B 
m 

8.3 

m of ta 
klime 




Aluminum, brown 

Babbitt's metal 

Brass, common . 

hard! '. '. 

" instruments 

" locom. bearings 

'* Pinchbeck 

*' red Tombac 

*' rolled 


, 


5 


" Tutenag 

" very tenacious.. 
'* wheels, valves.. 
II white 




" wire ... v. ....... 




'* yellow, fine 

Britannia metal 

When fused add... 
Bronze, red 








yellow 

'* gun-met., large 

*' " " small 

" ** soft.. 

'* cymbals 

" medals 

" phosphor 

*' statuary 

Bush-metal 


a 


u 

1—1 





Chinese silver 


11.1 


" white copper.. 
Church-bells 

Clocks, musical bells . . 
Clock-bells 


I 

1.5 


German silver 


'z.k 


" " fine 

Gongs 

Gun-metal 


rtn 


2.5 


House-bells 




Lathe-bushes 




Machinery bearings .... 

" " hard 

Metal that expands l 

in cooling f 

Muntz metal,10 oz. lead 
Pewter, best 

Sheathing-metal 

Speculum "" 

Steam-metal 


] 


6.7 

14" 

>5" 
2.5 

)6 8 


G 

< 
12* 


Telescopic mirrors . . 

Temper 

Type-metal and sle- ) 

reotype plates f 

White metal 




" " hard 

Oreide 





rea 
uic 


r.'.6.fi 
..1.3 



* Cu = copper; Zn = zinc; Sn = tin; Ni = nickel; Pb = lead; Sb = anti- 
mony; Bi = bismuth; Al s aluminum. 



144 



METALS. — SOLDERS. 



Solders. 

Solder is the name given to several different alloys used for 
the purpose of making joints between pieces of metal. 

The composition of the solder used in connection with the dif- 
ferent metals varies immensely, and the proportions in which 
each different kind of solder is mixed also vary according to 
circumstances. 

Solder must be more fusible than the metals it is intended to 
unite. 

Hard solders are those which fuse only at a red heat. 

Soft solders melt at a very low degree of heat. 

Table 21. 

COMPOSITION OF SOLDER. 



® ft 


Name or Use. 


^1 


^1 


6^ 

^1 


Is 


is 


c3 CO 


0^ 


482° F. 
350 " 
372 '' 
200 " 


Plumbers', coarse (hard) 

" fine (soft) 

•' fusible 

'* very fusible. . . 

For brass 


25 
67 
50 
25 


75 
33 
50 
25 

*75* 


*33* 
■33' 


'56* 

"m 


*67' 


*67' 






'' tin 


25 

47 












" copper 


58 




" (hard) 


67 



Soldering. — The surfaces to be united must be perfectly clean 
and freed from oxide, which would prevent adhesion and the for- 
mation of an alloy between the solder and the metal. 

As the surfaces when heated are very easily oxidized, they must 
be protected at the time. This is done by means of a flux which 
covers the surface and protects it from the air. 

Fluxes for Soldering. — The flux is varied according to the 

metals to be united. 

Metals. Fluxes. 

Copper and brass \ SaUammoniac, chloride of 

^^ ( zmc, or rosm 

Tinned iron Chloride of zinc or rosin 

Zinc Chloride of zinc 

Lead Tallow or rosin 

Lead and tin Rosi:i and sweet oil 

Soldering- fluid is a concentrated solution of chloride of zinc. 



TESTS OF MATERIALS. 145 

Tests for Materials. 

The tests to which materials used for specific purposes are sub- 
jected are ordinarily as follows: 

Axles. — Drop test, with tension test if further knowledge is 
desired. 

Boiler Iron. — Plates by tension, forging, and punching 
tests, and bending cold and hot. Shapes, the same, with welding 
test if shape is to be welded in use. Rivets y by tension, bending, 
and forging. 

Boiler Steel. — Tension, hardening, and forging tests, and 
bending hot and cold. 

High Structural Steel. — Tension, bending, and hardening. 

Mild Structural Steel. — Tension and bending tests, with 
welding, hardening, and annealing test if the metal is to be used 
for welded members. 

Structural Iron. — Tension, bending, and welding tests. 

Ship Material. — Plates^ tension and cold bending tests. 
Shapes, tension and hot and cold bending tests. Biveis, tension, 
bending, and forging tests. 

Rails. — Drop test and bending test, with tension test if further 
Information is desired. 

Tires. — Drop test, with tension test for further knowledge. 

Wire. — Tension and winding tests, and tests by bending back 
and forth around a turned stud of same diameter as the wire. 

Wire Rope. — Tension and longitudinal impact tests. 

Steel Pins. — Test-specimens are usually cut from the ends of 
blooms which have been forged into sizes convenient for the pur- 
pose. Tested by tension and bending. Pius of over 6 inches 
in diameter are in most cases drilled through their larger axis 
with holes from J inch to IJ inches in diameter, for the purpose 
of testing the soundness through the entire length. 

Bolts and Rivets. — Tension, shearing, and forging tests. 

Cast Iron. — Tension, bending, and compression tests. 

Copper Alloys and Soft Metals. — Tension and compres- 
sion tests. 

Woods. — Tension, compression, and transverse tests. 

Cements and Mortars. — Tension and compression tests. 

Building Bricks and Stones. — Compression and transverse 
tests. 

Paving Bricks and Stones, — Compression, transverse, im- 
pact, and abrasion tests, 



146 TESTING STRENGTH OF MATERIALS. 



Testing Strength of Materials, 

Tiie tests to which structural materials arc subjected in order 
to ascertain their s'reugth or resistance to deformation when in 
use are : tests for compression, or resistance to crushing; tension, 
uY resistance to teaxing asunder ; and flexion, or resistance to 
breaking under transverse strain. 

The testing is performed in suitable machines provided with 
apparatus for measuring the force of the required stress. Several 
forms of these machines are in the market and descriptions can 
be obtained from the manufac turcrs. 

The preparing of the specimens, carrying out the test, and 
interpreting the results require great care and study to avoid the 
reaching of erroneous conclusions, and should not be undertaken 
by those not thoroughly acquainted with the subject and with 
the particular material lo be tested. 

The testing-machine should be tested to determine whether its 
weighing apparatus is accurate, and whether it is so made and 
adjusted that in the test of a properly made specimen the line of 
strain is absolutely in line with the axis of the specimen. If it is 
not the result will be erroneous, because, the stress not being 
uniformly distributed on the cross-section, one side will have to 
yield prematurely, and thus the resistance of the specimen will 
be overcome in detail ; for want of attention to this particular 
many tests do not afford reliable results. 

The speed with which the load is applied is an important ele- 
ment and should be carefully noted and recorded. 

In tensile tests wrought iron and soft steel can be made to show 
a higher strength by keeping them under strain for a greater 
length of time. The pulling speed should not be less than half 
an inch per minute and not more than three inches per minute. 

In testing soft alloys — copper, tin, zinc, and the like — which 
flow under constant strain their highest apparent strength is 
obtained by testing them rapidly. 

Test-specimens. — In determining the size of the specimens 
for tensile tests the strength of the machine must first be taken 
into account. It is extremely convenient and it simplifies the 
subsequent calculation to make them of such a size that their 
sectional area will be a convenient multiple or fraction of a square 
inch. 

Tension. — The form of test-piece generally adopted for flat 
bars, plates, and shapes is a parallel strip which varies in length 



TESTING STRENGTH OF MATERIALS. 147 

according to the capacity of the machine on which it is to be 
tested. The ends are j-shaped by cutting fillets with a radius of 
about half an inch, so that the jaws of the machine can take a 
firm grip. In some cases the specimens are turned in a lathe to 
the required dimensions and forms. The section should be uni- 
form for not less than five inches of its length. 

The data obtained from a tensile test are : 1. Tensile strength 
in pounds per square inch of original area. 2. Elongation per 
cent of a stated length between gauge-marks, usually 8 inches. 
3. Elastic limit in pounds per square inch of original area. 

In order to be able to compare records of elongation it is nec- 
essary not only to have a uniform length of section between 
gauge-marks, but to adopt a uniform method of measuring the 
elongation to compensate for the difference between the apparent 
elongation when the piece breaks near one of the gauge-marks 
and when it breaks midway between them. The following 
method is recommended (Trans= A. S. M. E., Vol. XI, p. 623): 

Mark on the specimen divisions of ^ inch each. After fracture 
measure from the point of fracture the length of eight of the 
marked spaces on each fractured portion (or 7 + ^n one side and 
8 + on the other if the fracture is not at one of the marks). The 
sum of these measurements, less 8 inches, is the elongation of 8 
inches of the original length. If the fracture is so near one end 
of the specimen that 7 -|- spaces are not left on the shorter por- 
tion, then take the measurement of as many spaces (with the 
fractional part next to the fracture) as are left, and for the spaces 
lacking add the measurement of as many corresponding spaces of 
the longer portion as are necessary to make the 7 -\- spaces. 

During the performance of the test the operator has to watch 
carefully the behavior of the specimen in order to note its gen- 
eral character. Special care is required to note the reaching of 
the elastic limit, or the point at which the rate of stretch or other 
deformation begins to increase. When this point is reached the 
future behavior of the material will altogether depend on its pre- 
cise nature. If it is of a soft and ductile nature it will be drawn 
out to a small diameter in the neighborhood of the point of frac- 
ture before the final rupture takes place. If it is hard and rigid 
it may not be drawn out to any great extent, but may break, with 
very little reduction of area, and exhibit a high tenacity. 

As the critical point is being approached the utmost care has 
to be observed to avoid rashness in the application of the weight 
and to secure reliable results. 



148 CONTRACTION OR SHRINKAGE OF METALS. 

Ccmpression. — Specimens for ascertaining the resistance to 
compression are generally made in the form of cylinders, cubes, 
or rectangular prisms with square ends, of such dimensions as 
can be overcome by the power of the testing-machine. 

The dimensions of the specimen and its behavior, i.e., how it 
splits or fractures, bulges, bends, buckles, or flattens, and the 
loads which produce such eii'ucts, are noted. 

Transverse Strength. — Tests for resistance to transverse strain 
are made on prismatic bars, whose ends rest on knife-edges, and 
have a strain imposed at the centre, either by loading a plate 
suspended on a knife-edge or by means of levers. 

The dimensions of the specimen, distance between supports, 
deflection, and breaking weight are the points to be noted. 

Impact or Drop Tests are applied on full- sized specimens 
by means of a weight falling through a given distance (usually a 
weight of one ton falling through a distance of from 20 to 30 
feet). The number of blows required to cause rupture, the 
behavior of the material under the blows, the character of the 
fibre, and the contraction of area are noted. The specimen is so 
arranged that the blows act in the direction of its length. 

Contraction or Shrinkage of Metals, 

The allowance necessary for shrinkage varies for different 
kinds of metal and the different conditions under which they are 
cast. For castings where the thickness runs about one inch, cast 
under ordinary conditions, the following allowance can be made ; 

For cast iron J inch per foot 

brass y\ " '* 

copper y\ t< *< 

steel I '' " 

lead j% '' '* 

malleable iron- ^ " ** 

zinc , j\ '* ** 

tin t\ •• " 

aluminum y\ *' ** 

britannia -^^ " ** 

Thicker castings under the same conditions will shrink less 
and thinner ones more than this standard. The quality of the 
material and the manner of moulding and cooling will also make 
a difference. 



CONTRACTION" OR SHRINKAGE OF METALS. 



149 



To COMPUTE Weight of Cast Metals by Weight of 
Pattern.— Multiply weight of pattern by the following coeffi- 
cients : 

Cast Iron. 

Pattern made of CoefiBcient, 

White pine 14 

Oak 9 

Beech 9.7 

Birch. 10.6 

Linden 13.4 

Alder 12. 6 

Pear 10 

Brass. 
White pine 15 

Lead. 
White pine 23 

Tin. 
White pine 14 

Zinc. 
White pine 13.5 

Very accurate results cannot be expected, as the specific gravity 
of wood as well as of the metal fluctuates. 

Reductions for Bound Cores and Core-prints, — Multiply the 
square of the diameter by the length of the core in inches, and 
the product by 0.017 is the weight of the pine core to be de- 
ducted from the weight of the pattern. 

WEIGHT OF CASTINGS DETERMINED FROM WEIGHT OF PATTERN. 



A Pattern Weighing One 


Will Weigh when Cast in 


Pound made of 


Cast Iron. 


Zinc. 


Copper. 


Yellow 
Brass. 


Gun- 
metal. 


Mahogany, Nassau 

*' Honduras 

" Spanish 

Pine red 


Lbs. 
10.7 
12.9 
8.5 
12.5 
16.7 
14.1 


Lbs. 
10.4 
12.7 
8.2 
12.1 
16.1 
13.6 


Lbs. 
12.8 
15.3 
10.1 
14.9 
19.8 
16.7 


Lbs. 
12.2 
14.6 
9.7 
14.2 
19.0 
16.0 


Lbs. 
12.5 
15.0 
9.9 
14.6 


*' white 


19.5 


" yellow 


16.5 







150 MISCELLAKEOUS MATKKIALS. — SAKD. 



VII. MISCELLANEOUS MATERIALS. 

Sand. 

Sand is an aggregation of loose, incoherent grains of a crystal- 
line structure, derived from the disintegration of rocks and other 
mineral matter. It is called '* silicious," *' argillaceous," or 
•'calcareous," according to the character of the rock from which 
it is derived. It is obtained from pits, beds of rivers, the sea- 
shore, or may be made by grinding sandstones. The sand 
derived from the quartzose rocks is the most preferred for build- 
ing purposes. As substitutes for sand, scoriae, slag, cinder, and 
burnt clay are frequently used. 

Pit-sand has an angular grain and a somewhat rough surface, 
but often contains clay and organic matter; when washed and 
screened it furnishes a good sand for general purposes. 

River-sand has more or less rounded grains, and may or may 
not contain clay or other impurities. It is commonly of fine 
grain, is often white in color, and when clean is suited for plas- 
tering. 

Sea-sand has also more or less rounded grains. It contains 
alkaline salts, which attract and retain moisture and cause efflor- 
escence when used in brick masonry. 

Both sea- and river-sand are deficient in the sharpness required 
for good mortar on account of the attrition they are exposed to, 
but they are suitable for plastering, and in many localities the 
lack of more suitable material obliges their use for mortar, in 
which case they should be thoroughly washed. 

Use of Sand. — The uses of sand are various, as for mortar, 
for distributing the pressure of structures in soft soils, as a founda- 
tion and joint-filling for block and brick pavements, as piles in 
foundations, for plaster, etc. 

The use of sand in mortar is to prevent excessive shrinkage, 
and to save the cost of lime or cement. Ordinarily it is not acted 
upon by lime, its presence in mortar being purely mechanical. 
Rich lime adheres better to the surface of sand than to its own 
particles, hence it is considered to strengthen lime mortar. 
With cement it weakens the mortar. 



MISCELLANEOUS MATERIALS. — SAND. 



151 



Size of Sand. — "When the grains of sand range from ^^^, to | 
inch it is called** coarse " sand; when from ^V to ^^, " fine " sand; 
and from 3^ to ^V *' ^^^T fi^e" sand; and when composed of sizes 
varying within these limits, " mixed " sand. 

The Fineness of sand is measured by passing through sieves 
having the following dimensions: 

Table 22. 
SIZE OF SIEVES FOR SIFTING SAND 



Number of 
Sieve. 


Number of 


Number of 


Length of Side 


Diameter of 


Holes per 


Holes per 


of Hole. 


Wire. 


Lineal Inch. 


Square Inch. 


Inch 


Inch. 


1 


20 


400 


.03101 


.01899 


2 


30 


900 


.02119 


.01214 


3 


50 


2500 


.01119 


.00881 


4 


80 


' 6400 


.00599 


.00051 


5 


170 


28900 


.00309 


.00279 



Weight of Sand. — Dry sand weighs from 80 to 115 pounds 
per cubic foot, or about one to one and a half tons per cubic 
yard. 

The YoiDS of ordinary sand range from 0.3 to 0.5 of the volume,, 
The more uneven the grains in size the smaller the percentage of 
voids. 

Testing Sand. — The Cleanness of sand may be tested by 
rubbing a little of the dry sand in the palm of the hand, and aftei* 
throwing it out noticing the amount of dust left on the hand. 
The cleanness may also be judged by pressing the sand between 
the fingers while it is damp; if the sand is clean it will not stick 
together, but will immediately fall apart when the pressure is 
removed. 

The Sharpness of sand can be determined approximately by 
rubbing a few grains in the hand or by crushing it near the ear 
and noting if a grating sound is produced; but an examination 
through a small lens is better. 

To DETERMINE THE PRESENCE OF SaLT AND ClAY. — Shake up 

a small portion of the sand with pure distilled water in a perfectly 
clean stoppered bottle, and allow the sand to settle ; add a few 
drops of pure nitric acid and then add a few drops of solution of 
nitrate of silver. A white precipitate indicates a tolerable 
amount of salt; a faint cloudiness may be disregarded. 

The presence of clay may be ascerlained by agitating a small 
quantity of the sand in a glass of clear water and allowing it to 



152 MISCExjLANEOUS materials. — GRAVEL. 

Stand for a few hours to settle; the sand and clay will separate 
into two well-defined layers. 

Preparation of Sand. — Screening. — Sand is prepared for 
use by screening to remove the pebbles and coarser grains. The 
fineness of the meshes of the screen depends upon the kind of 
work in which the sand is to be used. 

Washing. — Sand containing loam or earthy matters is cleansed 
by washing with water, either in a machine specially designed 
for the purpose and called a sand-washer, or by agitating with 
water in tubs or boxes provided with holes to permit the dirty 
water to flow away. 

Drying. — When dry sand is required it is obtained by evapor- 
ating the moisture either in a machine called a sand-dryer, or by 
heating the sand in large shallow pans of wrought iron or on 
sheets of boiler-plate supported on stones with a wood fire placed 
underneath. 



Oravel, 

f Gravel is an accumulation of small rounded stones which vary 
in size from a small pea ta a w^alnut or something larger. It is 
often intermingled with other substances, such as sand, loam 
clay, etc., from each of which it derives a distinctive name. 

The uses of gravel are various, as: for concrete, for lining at 
the back of retaining walls and slope pavements, as a filling with 
bituminous cement for the joints in block pavements and for tar 
and asphalt roofs, etc. 

For use it is assorted into different sizes by screening and whec 
necessary washed. 

Weight of Gravel. — A cubic yard of pit-gravel weighs 
about 3300 pounds; mixed with clay it weighs about 155 pounds 
per cubic foot. 

Shingle is the small stones found on the shores of rivers or the 
sea. 

Grit is fine gravel, the pebbles of which do not exceed one half 
inch in diameter. The name grit is also applied to hard sand- 
stone. 



MISCELLANEOUS MATERIALS. — CLAY. 153 



Clay. 

Pure clay consists of a hydrated silicate of alumina in com- 
bination with other substances derived from the felspathic rocks, 
which by their disintegration and decomposition have formed 
clay. The purest form of clay containing the largest proportion 
of alumina is known as kaolin, the name of a mountain in China 
where a pure white clay is worked; it is a pure white, dull, 
earthy, unctuous substance. 

Pure clay is soft, more or less unctuous to the touch, white 
and opaque, and when breathed upon emits a characteristic odor. 
It is infusible and insoluble either by water, nitric or hydrochloric 
acid. It may be converted by water into a doughy, tenacious, 
plastic mass. It absorbs water with avidity, but when burned 
at a sufficiently high temperature it becomes hard and brittle and 
loses almost wholly or altogether this property of combining with 
water. 

In nature the greater number of clays are found intermingled 
with other substances foreign to them in their original localities. 

The usual constituents of clay are alumina, silica, iron, lime, 
magnesia, and alkalies, all of which modify the character of the 
clay and its applications, according as one or other of these ingre- 
dients predominates. 

Clay and sand mechanically mixed constitute loam; clay and 
carbonate of lime mechanically mixed, marl. 

Clay is of various colors, as red, blue, brown, yellow or ochre, 
and variegated. The color is due to the presence of metallic 
oxides, usually iron and some organic substances. 

Refjiactory Clays are those which resist fusion by the great- 
est heat of an ordinary furnace. They consist mainly of alumina 
and silica, the silica predominating. They are used for the manu- 
facture of fire-bricks and crucibles. 



154 GYPSUM — PLASTER OF PARIS — MINERAL WOOL. 



Gypsum— Plaster of Paris. 

Gypsum is a compound of sulphate of lime with water. It is 
found stratified and in various conditions : crystalline, laminated, 
granular, and earthy. It is translucent, usually white or gray, 
has a pearly lustre, and can be easily scratched with a knife. 

B}^ calcining gypsum the water is expelled, and it becomes a 
dry white powder of sulphate of lime, known as "plaster of 
Paris." When this powder is rapidly mixed with water so as to 
form a paste it immediately begins to combine with a part of the 
water, so as to reproduce gypsum in a compact granular state; 
heat is at the same time developed, which hastens the evaporation 
of the superfluous water. The mixture should be made by putting 
the powder into the water, not the water amongst the powder. 

The principal use of plaster of Paris is for plastering and inte- 
rior decoration. (See under Plastering.) 

Mineral Wool. 

Mineral wool, slag wool, or silicate cotton is a glass-like fibre 
produced from blast-furnace slag. The process consists in sub- 
jecting a small stream of the molten slag to the force of a jet of 
steam or compressed air, which divides it into innumerable 
small shot or spherules, forming a spray of spark-like objects. 
Threads are formed and detached from the main body of the 
stream, their length and fineness being dependent upon the 
fluidity and composition of the material under treatment. When 
the slag is of the proper consistency the spherules are small at 
the outset, and are to some extent absorbed into the fibre, but 
in no case will they entirely disappear ; so that a great portion 
of the wool contains them they are separated by riddling. That 
portion of the thread which is carried away and separated from 
the shot by the air- currents is very light, weighing about 14 
pounds per cubic foot, and forms the grade called "extra" 
grade; the balance of the fibre weighs about 24 pounds per cubic 
foot, and is called " ordinary " grade. A cubic foot of the slag 
weighs about 192 pounds. In the manufacture of mineral wool 
slags of a slightly acid composition are preferred, though it is said 
that any scoriaceous substances can be used. 

When gathered up the threads and fragments appear to lie in 
all possible directions with relation to each other, in consequence 



MISCELLA:NrEOUS MATERIALS. — MI^-ERAL WOOL. 155 

of which there is no parallelism or common direction to the 
threads, so that the air-spaces are angular in shape and micro- 
scopic in size. The wool is collected in a large chamber, where it 
settles in a bulky stale, having a fleecy appearance. About 80 
per cent of the product has to be riddled. 

The fibres or threads vary in thickness from that of common 
spun glass to an extreme tenuity, represented by fractions of a 
thousandth of an inch. The bulbs may be generally described as 
solid bodies containing more or less numerous vesicles or hollows; 
the more solid ones are transparent or show iridescence. 

Mineral wool is fire- and vermin -proof, and is used for insulat- 
ing heated surfaces, for protection against cold, deadening sound, 
fiire-proofing, vermin-proofing, and for cleaning galvanized wire, 
etc. It is applied loose. But, although one of the most valuable 
non-conducting substances, it requires to be used with precaution 
against the absorption of moisture, in which case it is liable to 
decompose, the sulphur originally contained in the slag oxidizing 
to sulphuric acid, and forming soluble sulphates, which attack 
the metallic surfaces with which the wool is in contact. It has been 
found that not only the mineral acids, but also organic acids, are 
capable of decomposing it in the presence of moisture and heat, 
and the fine fibrous condition of the wool renders it still more 
subject to decomposition than solid slag. As the non-conducting 
property depends upon the interstitial air-space, it is essential tha^ 
it should not become packed. 

One ton will cover about 1800 square feet one inch thick. 

"Extra "grade is put up in bags containing from 25 to 45 
pounds; each; "ordinary" grade is put up in bags containing from 
60 to 90 pounds. 



15G MISCELLA]^EOUS MATERIALS. — ASBESTOS— TaK. 



Asbestos. 

Asbestos 13 a fibrous mineral composed principally of silica 
and magnesia. It consists of fine crystalline fibres which vary 
greatly in character, being sometimes of a long staple or fibre, 
and sometimes flocculent or like woody fibre, or resembling clay 
or soapstone, or even in a granular form. In color it ranges 
from white with greenish and metallic reflections through man}*- 
shades of yellow to dull brown or reddish. The reddish varieties 
appear to be colored with an admixture of oxide of iron. The 
most valuable property of asbestos is its power to resist high 
temperatures, which is indicated by its name "unconsumable.'* 
Some varieties are unaffected by a heat up to 2000° F. Other 
kinds can only be fused at 3000° F., and some kinds have been 
submitted to a temperature of 5000° F. without apparent change. 
Some kinds when heated to a sufficient temperature to drive off 
the contained water become brittle and may easily be crumbled 
between the finger and thumb. As a rule it fuses with difficulty 
before the blowpipe. It feels soft and greasy to the touch, like 
soapstone or talc, but is clean, and in the form of flour can be 
rubbed away between the fingers to an invisible powder. 

The mineral when consisting of long, tough, and flexible fibres 
is usually distinguished from the commoner varieties of asbestos 
by the name ** chrysotile." Such material is used for weaving 
into fabrics. 

Tar. 

Coal-tar is produced as a by-product in the manufacture of 
gas from coal. When distilled it produces, in various stages, 
first, coal-7Lap7itlia, which is useful for dissolving rubber, etc.; 
then dead-oil or creosote, used for preserviug timber ; and lastly, 
tar or pitch, which is used for rooting, waterproofing walls, etc. , 
and as an ingredient for varnishes, and for filling the joints in 
stone-block pavements, coating cast-iron pipes, etc. 

Coal-tar is very brittle at the freezing-point and softens and 
flows between 70° and 115° F. It has a strong pungent odor. 

Paving Pitch, used for filling joints in stone-block pavements, 
etc., is the residue obtained from distilling coal-tar, and is desig- 
nated as Distillate No. 1, 2, 3, etc., according to its density or 
specific gravity. The character of the distillate varies with the 
system and temperature employed. 



MtSCELLAKEOtrS MATERIALS. — CREOSOTE. 157 

Wood- TAR is produced by the dislillatioii of pine and other 
resinous trees; the residue left after distiUation is called pitch. 

Mineral Tar is obtained by distilling bituminous shales (see 
Asphaltum). 

Creosote. 

Creosote oil is a product obtained in distilling coal-tar. It is 
an oily liquid, varying in composition according to the quality 
of the coal from whi^h it is obtained, and containing hydro- 
carbons of different degrees of volatility and varying antiseptic 
qualities. 

The requisites for creosote oil used in the preservation of 
timber are: 

To contain 8 per cent of tar acids by analysis with caustic soda 
and sulphuric acid. 

To be quite liquid at 100° F. and without deposit until the tem- 
perature falls to 95° F. 

One fourth not to distil over in a retort at less temperature 
than 600° F., and this fourth to be heavier than water. 

To be free from adulteration with bone-oil, shale-oil, or any oil 
not distilled from coal-tar. 

The minute glistening cubes generally observable on freshly 
creosoted wood consist of naphthaline, a substance that possesses 
considerable antiseptic properties ; when this substance exists in 
the liquid creosote in moderate quantities it thickens and confirms 
its consistency, but when there is a very large proportion it makes 
the creosote too* solid. 

WooD-CREosoTE OiL is a product of the distillation of wood* 
tar obtained from the resinous woods, as Georgia pine, etc. It 
has a specific gravity of about 1.05, is still fluid at 15° F., boils 
at 230° F., contains 5 per cent of tar, 45 per cent of tar acids, 50 
per cent oils, has a peculiar penetrating odor and hot taste. 

Patented preparations of wood creosote, sold under the names 
ot fernoUne, woodiline^ etc., are extensively used as a preservative 
for wood. 



158 SHEATMING-FELTS AKD -PAPERS. 



Slieathiiig-felts and -papers. 

Felt. — The better qualities of felt are made from hair cemented 

together with asphaltic cement ; the commoner varieties are com- 
posed of waste vegetable fibres cemented together with asphaltum, 
coal-tar, or rosin. 

Asphalt Felt is prepared by saturating felt with asphaltum 
either alone or mixed with petroleum residuum. It is black or 
nearl}' black in color and has a strong odor of asphaltum. 

Tak Felt is prepared by saturating felt with coal-tar. 

Asbestos Felt is prepared from fibrous asbestos cemented 
together with various cementing materials. 

Papers. — Sheathing-papers are made from Manila hemp and 
other vegetable substances treated with various compounds (such 
as certain compounds of copper and ammonia), the effect of which 
is to coat and impregnate them with a varnish-like substance 
(cupro-cellulose) which enables them to resist the weather. 

The papers are made in one, two, or three thicknesses and are 
designated as **one-ply," "two-ply," etc. 

The cheaper grades of paper are made waterproof by saturat- 
ing them with various rosins and some earthy material as a filler. 
Waste oils are also used. 

Asbestos Paper is manufactured from asbestos cemented by 
various cementing materials. 

Tarred Paper is prepared by saturating Manila or other paper 
in coal-tar alone or mixed with lime and residuum oils. 

Rosix-sizED Papers are made by immersing Manila or other 
'paper in a mixture of rosin, glue, and ochre. 



MISCELLAKEOUS MATERIALS.— GLUE. 159 



Glue. 

Glue is prepared from waste pieces of skins, horns, hoofs, and 
other animal offal. 

These are steeped, boiled, strained, melted, reboiled, and cast 
into cakes, which are then dried. 

The strongest kind of glue is made from the hides of oxen, 
that from the bones and sinews is weaker ; the older the animal 
the stronger the glue. 

Good glue should be hard in the cake, of a strong dark color, 
almost transparent, free from black or cloudy spots, and with lit- 
tle or no taste or smell. 

The best varieties are transparent and of a clear amber color. 

Inferior kinds are sometimes contaminated with the lime used 
for removing the hair from the skins of which they are made. 

The best glue swells considerably (the more the better) when 
immersed in cold water, but does not dissolve, and returns to its 
former size when dry. 

To prepare glue for use it should be broken up into small 
pieces, and soaked in as much cold water as will cover it for 
about twelve hours. 

It should then be melted in a double glue-pot, covered, to pro- 
tect the glue from dirt. Care must be taken that the outer vessel 
is full of water, so that the glue shall not burn or be brought to 
a temperature higher than that of boiling water. 

The glue should be allowed to simmer for two or three hours, 
then gradually melted ; then a small quantity of boiling water is 
added to make the glue liquid enough to run off a brush in a 
continuous stream without breaking into drops. 

Freshly melted glue is stronger than that which has been 
repeatedly remelted. 

Frequent remelting impairs the quality of the glue. This may 
be known to be the case when it becomes of a dark and almost 
black color. 

To secure the full effect of the adhering qualities of glue it is 
necessary that it be thoroughly melted and used while boiling 
hot; that the wood to be united be perfectly clean, dry, and 
warm ; that the surfaces of each piece be covered evenly with a 
thin film and then brought together as tightly as possible, so that 
the suj)erfluous glue may be squeezed out. 



160 MISCELLANEOUS MATERIALS. — ROPE. 



Rope, 

Rope is the general name applied to cordage over one inch in 
circumference. 

The materials employed for making rope are various vegetable 
fibres. The strongest rope is made of liemp. Manila hemp and 
sisal hemp. For cords and twines phormium or New Zealand 
hemp, Russian hemp, and jute are largely used. These laiter 
varieties are also frequently employed to adulterate the stronger 
class of hemps. Ropes and twines of cotton are extensively 
made. 

A rope is composed of a certain number of "strands," the 
strand being itself made up of many "yarns." 

Ropes are designated by the method followed in their con- 
struction, as • 

Hawser-laid : Three strands of yarn twisted lefi-Xmnd, the yarn 
being twisted r^^7^^hand. 

Cable-laid : Three strands of hawser-laid rope twisted right- 
hand. 

Shroud-laid or four-strand consists of a central strand or core 
with four strands twisted around it. 

The twist in each successive operation is in a different direc- 
tion from the preceding, and this alternation of direction serves 
to some extent to preserve the parallelism of the fibres. 

A good hemp rope is hard but pliant, yellowish or greenish 
gray in color, with a certain silvery or pearly lustre. A dark or 
blackish color indicates that the hemp suffered from fermentation 
in the process of curing, and brown spots show that the rope was 
spun while the fibres were damp, and is consequently weak and 
soft in those places. Sometimes a rope is made with inferior 
hemp on the inside, covered with yarn of good material. This 
may be detected by dissecting a portion of the rope. Other in- 
ferior ropes are made from short fibres, or with strands of un- 
equal length or unevenly spun, the rope in the first place appear- 
ing woolly, on account of ends of fibres projecting, and in the 
latter case the irregularity of manufacture is evident on inspec- 
tion. 

A test for ascertainini^ tlic purity of Manila hemp rope con- 
sists in forming balls of loose fibre of the ropes to be tested and 
burning them completely to ashes : pure Manila burns to a dull 
grayish-black ash; sisal leaves a w^hitish-gray ash ; combinations 



MISCELLANEOUS MATERIALS. — ROPE. 



161 



of Manilla and sisal yield a mixed ash resembling the beard of a 
man turning from black to gray. Manila hemp is frequently 
adulterated with phormium (New Zealand flax) and Russian 
hemp, both of which are much inferior in strength. 

To compute tlie strain that can be borne with safety by new 
ropes, hawsers, and cables square the circumference of the rope, 
etc., and multiply it by theicoefficient given in Table 23. 

Table 23. 

COEFFICIENTS FOU COMPUTING THE SAFE STRAIN THAT MAY BE 
BORNE BY ROPES, HAWSERS, AND CABLES. 



Description. 



Circumference in ins. 



White rope, 2.5 to 6 ins. 

White rope, 6 to 8 ins 

White rope, 8 to 12 ins... 
White rope, 12 to 18 ins. 
White rope, 18 to 26 ins.. 
Tarred rope, 2.5 to 5 ins. 
Tarred rope, 5 to 8 ins. 

Tnrr*irl rr»r»A ft tr» 19 inc 



Tarrea rope, o to » ins. . 
Tarred rope, 8 to 12 ins. 
Tarred rope, 12 to 18 ins.. 
Tarred rope, 18 to 26 ins. 
Manila rope, 2.5 to 6 ins. . 
Manila rope, 6 to 12 ins.. . 
Manila rope, 12 to 18 ins.. 
Manila rope, 18 to 26 ins.. 



Ropes. 



White. Tarred 



Lbs. 
1140 
1090 
1045 



810 
760 



White Tar'd 



Lbs. 
1330 
1260 
880 



950 
835 



Lbs. 



855 
825 
780 



Lbs. 



1005 
940 
820 



Hawsers. 



Lbs. 
600 
570 
530 
550 



440 
465 



Lbs. 



460 
480 
505 



Cables. 



White Tar'd 



Lbs. 

'516 
530 
550 
560 



510 
535 
560 



Lbs, 



505 
525 
550 



When it is required to ascertain the weight or strain that can be 
borne by ropes, etc., in general use, the above units should be 
reduced one third, in order to meet the reduction of their strength 
by chafing and exposure to the weather. 



162 



MISCELLAN EOUS MATERIALS. — WIRE. 



Table 24. 

STRENGTH OF MANILA ROPE. 









Breaking Load. 








Breaking Load. 


Diam. 


Circ. 
Ins. 


Wt. per 
Foot. 
Lbs. 




Diam. 
Ins. 


Circ. 
Ins. 


wt. per 

Foot. 
Lbs. 




Ills. 


Tons. 


Lbs. 


Tons. 


Lbs. 


.239 


% 


.019 


.25 


560 


1.91 


6 


1.19 


11.4 


25536 


.318 


1' 


.083 


.35 


784 


2.07 


QV. 


1.39 


13.0 


29120 


.477 


ly. 


.074 


.70 


1568 


2.23 


7 


1.62 


14.6 


32704 


.636 


2 


.132 


1.21 


2733 


2.39 


IV. 


1,86 


16.2 


36288 


.795 


2V. 


.206 


1.91 


4278 


2.55 


8 


2.11 


17.8 


39872 


.955 


3 


.297 


2.73 


6115 


2.86 


9 


2.67 


21.0 


47040 


1.11 


SV. 


.404 


3.81 


8534 


3.18 


10 


3.30 


24.2 


54208 


1.27 


4 


.528 


5.16 


11558 


3.50 


11 


3.99 


27.4 


61376 


1.43 


4M 


.668 


6.60 


14784 


3.82 


12 


4.75 


30.6 


68544 


1.59 


5 


.825 


8.20 


18368 


4 14 


13 


5.58 


33.8 


75712 


1.75 


5% 


.998 


9.80 


21952 


4.45 


14 


6.47 


37.0 


82880 



The strength of Manila ropes is very variable. The above table 
supposes an average quality. Ropes of good Italian hemp are 
considerably stronger than Manila ; but their cost excludes them 
from general use. The tarring of ropes is said to lessen their 
strength ; and, when exposed to the weather, their durability 
also. The use of it in standing rigging is partly to diminish 
contraction and expansion by alternate wet and dry weather. 

The strengths of pieces from the same coil may vary 25 per cent. 

A few months of exposed work weakens ropes 20 to 50 per 

cent. 

STRENGTH OF BLOCKS, HOOKS, AND ROPES. 



Dimensions. 


Two Single Blocks. 


Two Double Blocks. 


Two Triple Blocks. 


^ 


® . 


"3 


'5 


'S 


B 


•3 


'5 




p.t-1 


u 


t- © 




h o 




I- d 


o 


§^ 


CO CO 


■s 1 


00 OS 


■S a 


(fa 03 


% K 


.2 


Pit 

oi 


.so§ 




log 

-3 ^ 


a o^ 


0) 






C/2 


















m 


m 


m 


m 


PQ 


M 


Ins. 


Ins. 


Pounds. 


Pounds. 


Pounds. 


Pounds. 


Pounds. 


Pounds. 


4 


* 


2,218 


3,600 


2,985 


7,200 


3,987 


10,800 


5 


« 


2,985 


6,400 


3,987 


12,800 


5,410 


18,200 


6 


f 


3,987 


8,100 


5,410 


16,200 


6,360 


24,300 


7 


* 


5,410 


12,100 


6,360 


24,200 


9,356 


36,300 


8 


1 


6,360 


14,400 


9,356 


28,800 


13,720 


43.200 


9 


n 


13,720 


19,600 


16,030 


39,200 


18,722 


58,800 


10 


n 


16,030 


22.500 


18,722 


45,000 


20,375 


67,500 


12 


n 


18,722 


28,900 


20,375 


57,800 


28,300 


86,700 


14 


H 


19,050 


32,400 


20,375 


64,800 


28,300 


97,200 



MISCELLANEOUS MATERIALS. — WIRE. 16.^^ 

The table on p. 162 gives the breaking-strain of hooks and 
shackles as tested by the United States Government; aJso the 
strength of new rope as adopted by the rope manufacturers. 
0;.e third the strength of new rope is considered the proper 
working-load. 

With a rope over a stationary sheave, one man will hoist 
nearly half his weight, averaging 75 pounds, barring friction. 
Friction reduces this force to about 60 pounds if the sheave be 
self- lubricating bronze or roller bushing, and to about 50 pounds 
if the sheave be common or iron bushed. Each sheave in the 
lower or movable block multiplies this force by two, so that one 
man should hoist with a pair of blocks as follows : 

Single iron bushed ^ 100 lbs. 

Double *' 200 '' 

Triple '' 300 '' 

Single S. L. bronze or roller bushed 120 *' 

Double '' ** 240 *' 

Triple '* ** 360 " 

It takes three men to hoist with a pair of single blocks the 
same load that one man will hoist with a pair of triple blocks. 

Wire. 

A rod, thread, or filament of various metals of uniform section, 
usually cylindrical; but various forms, such as oval, half round, 
square, and triangular, are also made. 

The earliest forms of wire were hammered from rough bars. 
This crude way was superseded later when it was discovered 
how to draw, and this method of wire -drawing is now universally 
applied for wires of any material. In the case of iron wire the 
metal is first converted from '* blooms" to ''billets" and from 
** billets" to rods at one heat. This is accomplished by a long 
train of rolls which pass the rods from one to the other. The 
rods average from 200 to 600 yards in length. Very large sizes 
of wire may be made by continued rolling of the rods. 

The rods thus produced by rolling in the heated state are 
made into wire by the process of ** cold -drawing." By this 
process the rods of iron or steel, rolled several hundred yards 
long, are first pointed at one end by hammering or by a special 
machine, and are then cleansed by washing in a bath of dilute 



lG2b MISCELLANEOUS MATERIALS. — WIRE. 

sulphuric acid or hydrochloric acid, and afterwards are immersed 
in lime water to give a drawing surface. After drying by heat 
they are ready for the drawing-mill, which consists of a series of 
horizontal drums or pulleys, 10 to 30 inches in diameter, termed 
*' blocks," mounted on vertical axes on long benches. Accom- 
panying each drum are draw-plates and pincer-drawers. The 
draw-plates are disks or blocks of cast steel drilled with tapering 
holes, the small ends of which correspond exactly to the size of 
wire to be drawn from it. The form of the hole, of course, de- 
termines the form of cross-section of the wire, which is usually 
circular, though not necessarily so. When the holes become 
worn from use and depart from their original gauge, the metal 
is hammered around the small end, closing it, after which it is 
reamed out to standard size. Where great uniformity of gauge 
is required, as in fine gold or platinum wire, perforated rubies 
or similar hard minerals are fitted in the draw-plate. The draw- 
plates are clamped in vises fixed to the bench. As the tapering 
end of the rod is inserted in the hole of the plate, mechanical 
pincers seize it and pull it through. The pincers are fixed on 
horizontal arms, which are moved backward by cams fixed on 
the axes which rotate the drums. The wire as it is pulled 
through by the pincers is wound on the drums. The bottom of 
the drum is fitted with recesses to correspond with projections 
on a cam mounted on the same axis. The drum can be raised so 
as not to be in contact with the cam, and then may be turned 
freely on a spindle. When enough wire has been drawn through 
the draw-plate by the pincers to make one turn round the drum, 
the wire is taken from the pincers and fastened to the drum, 
which is lowered, and the cam fitting in its base turns it and 
winds the wire upon the drum. The drums draw from 500 to 
700 feet per minute for ordinary wire, and somewhat slower for 
crucible steel. The wire has now been drawn down one size, 
reducing the diameter about 10 per cent, and the process is con- 
tinued until the proper gauge is attained. It is said that copper 
wire may be reduced 15 sizes at one drawing. In continuous 
wire-drawing several drums are placed in line on a frame so that 
the wire winds on and off each one successively. Between the 
drums rotating disks made of some extremely hard substance 
reamed out to size are placed so that the wire passes through 
them. The holes in the succeeding disks are smaller than those 
in the preceding ones. Thus the cross-section may be reduced 



MISCELLANEOUS MATERIALS. — WIRE. 162g 

a number of sizes in one operation. The drawing is facilitated 
by the application of lubricants: a kind of grease for the larger 
grades, and liquids, such as soapy water and milk, for the 
smaller. Where a straw-colored wire is not objectionable a weak 
solution of copper sulphate is used as the drawing liquor. These 
lubricants coat the wire with a mucilaginous or metallic film so 
as to preserve it from oxidation and leave a polished surface. 

Wire-drawing increases the hardness of the metal so that the 
wire has to be frequently annealed during the process. In prac- 
tice, fine wire is thus softened six or eight times. The anneal- 
ing pots consist simply of metal chambers into which the wire is 
placed, and the pot is then hermetically sealed. The process of 
heating requires several hours at a red heat, a temperature of 
600^ to 700° F. being best. The pots and their contents are then 
allowed to cool slowly. An average charge for a pot is two and 
a half tons of wire. 

When unprotected iron wire is stretched in the open air and 
exposed to the elements it loses in time a large part of its 
strength and conductivity, owing to oxidation or rusting. To 
prevent this oxidation it was formerly the plan to dip the wires 
while red hot in linseed oil, but galvanizing is now universally 
employed for this purpose. 

Steel commonly used in the wire trade contains from one tenth 
to 1 per cent of carbon. Four tenths per cent of carbon in the 
steel used would make steel spring wire, five tenths ordinary 
wire rope, and six tenths of 1 per cent piano wire. Where tough- 
ness is required the per cent of manga nese may range as high as 
seven tenths of 1 per cent. 

In America size 0000 is the largest, and 40 about the smallest 
in ordinary work. If a size larger than 0000 is required a cable 
composed of several wires is used. Much finer than size 40 is 
used for special purposes, as in telescopes and optical instruments, 
where the wire is much finer than a silk fibre. A human hair 
is -^^Q of an inch in diameter, while platinum has been drawn 
down to Yo^(jo of an inch, and by coating with silver and drawing 
and then dissolving the film of silver with acid, fibres of plat- 
inum ^-Q^-Qfj of an inch in diameter have been obtained. 

The variety known as improved steel wire implies that which 
has been treated by a patented process of annealing, hardening, 
and tempering, by which the wire may have its tensile strength 
increased without impairing its ductility appreciably, but usually 
at some sacrifice of toughness. 



162d MISCELLANEOUS MATERIALS. — WIRE. 

TTie tests of the quality of wire include, besides those for tensile 
strength, a number to determine its ductility and elasticity. 
It should be capable of being bent forward and backward at right 
angles to itself a certain number of times without breaking. It 
must be capable 'of being wound around a wire of its own diam- 
eter a certain number of times without showing signs of splitting, 
and it should be able to bear a certain number of twists in a 
given length without splitting. The elongation is also important, 
particularly in wire for telegraph use, where the specifications 
call for from 12 to 20 per cent elongation. 

The process of wire-drawing greatly increases the strength of 
the material from which it is drawn. Thus it has been found 
possible to temper steel wire to sustain a load equivalent to 190 
tons per square inch, while 70 tons is considered large in test 
pieces of hard steel. Such wire, however, is not of practical 
use, because it is exceedingly brittle, and the brittleness increases 
very rapidly in proportion to the strength towards this limit. 
A strength of 150 tons is considered the greatest that can be 
combined with the essential ductility and elasticity. 

Copper wire is manufactured by rolling ingots or billets into 
rods in the hot state, and drawing them as in the case of iron 
wire. 

Of the other metals and alloys employed in the manufacture 
of wire, the most important is silicum bronze. It is formed by 
adding silicum to copper. The properties of this metal show a 
conductivity of 40 to 98 per cent of copper — three to six times 
that of iron, although only one fourth the weight — and tensile 
strength nearly equal to that of steel, and does not oxidize 
readily. 

The sizes of wires are estimated by certain more or less recog- 
nized standard wire gauges. The most commonly quoted is the 
Birmingham wire gau^^e. It gives forty measurements, which 
bear no definite relation to each other, ranging from the largest. 
No. 0000 r3 .454 inch, to No. 36 = .004 inch. The Brown & 
Sharpe gauge is also extensively recognized. In it the gradations 
are uniform, increasing in geometric ratio, so that the size of 
each successive number is found by multiplying the preceding 
by 1.123. The standard is calculated from wire No. 36, which 
represents a diameter of .005 inch. 

The following table gives the dimensions of each size of several 
of the gauges in ordinary use : 



\ 



MISCELLANEOUS MATERIALS. — WIRE, 



163 



Table 25. 
WIRE AND SHEET-METAL GAUGES COMPARED. 



o . 




hi 




§ 22 . 


British Imperial 
Standard 


dard 
or 

Plate 
Jteel. 
dard 
1893. 


O . 


© be 


-^3 




M 3 


'i p^l 


Wire Gauge. 


n «w _^ ^^ c ^- 

•^ (D ii TT^ >^ 






cO 


.s-S 


a !«>§ 


Legal Standard 




C ei3 


30 




f 


1 M- 


in Great Britain 

since 

March 1, 188i 


h 




Inch. 


Inch. 


Inc 


h. Inch. 


Inch. 


Millim. 


Inch. 




0000000 






.49 




.5 


12.7 


.5 


7/0 


000000 






.46 




.464 


11.78 


.469 


6/0 


00000 






.43 


!45* 


.432 


10.97 


.438 


5/0 


0000 


■';454" 


.'46"" 


.39 


3 .40 


.4 


10.16 


.406 


4/0 


000 


.425 


.40964 


.36 


2 .36 


.372 


9.45 


.375 


3/0 


00 


.38 


.3648 


.33 


1 .33 


.348 


8.84 


.344 


2/0 





.34 


.32486 


.30 


7 .305 


.324 


8.23 


.313 





1 


.3 


.2893 


.28 


3 .285 


.3 


7.62 


.281 


1 


2 


.284 


.25763 


.26 


3 .265 


.276 


7 01 


.266 


2 


3 


.259 


.22942 


.24 


4 .245 


.252 


6.4 


.25 


3 


4 


.238 


.20431 


.22 


5 .225 


.232 


5.89 


.234 


4 


5 


.22 


.18194 


.20 


7 .205 


.212 


5.38 


.219 


5 


6 


.203 


.16202 


.19 


2 .19 


.192 


4.88 


.203 


6 


7 


.18 


.14428 


.1? 


7 .175 


.176 


4.47 


.188 


7 


8 


.165 


.12849 


.16 


2 .16 


.16 


4.06 


.172 


8 


9 


.148 


.11443 


.14 


8 .145 


.144 


3.66 


.156 


9 


10 


.134 


.10189 


.13 


5 .13 


.128 


3.26 


.141 


10 


11 


.12 


.09074 


.12 


.1175 


.116 


2.95 


.125 


11 


12 


.109 


.08081 


.10 


5 .105 


.104 


2.64 


.109 


12 


13 


.095 


.07196 


.09 


2 .0925 


.092 


2.34 


.094 


13 


14 


.083 


.06408 


.08 


.08 


.08 


2,03 


.078 


14 


15 


.072 


.05707 


.07 


2 .07 


.072 


1.83 


.07 


15 


16 


.065 


.0508-2 


.06 


3 .061 


.064 


1.63 


.0625 


16 


17 


.058 


.04526 


.05 


4 .0525 


.056 


1.42 


.0563 


17 


18 


.049 


.0403 


.04 


7 .045 


.048 


1.22 


.05 


18 


19 


.042 


.03589 


.04 


1 .04 


.04 


1.01 


.0438 


19 


20 


.035 


.03196 


.03 


5 .035 


.036 


.91 


.0375 


20 


21 


.032 


.02846 


.03 


2 .031 


.032 


.81 


.0344 


21 


22 


.028 


.02535 


.02 


8 .028 


.028 


.71 


.0313 


22 


23 


.025 


.02257 


.02 


5 .025 


.024 


.61 


.0281 


23 


24 


.022 


.0201 


.02 


3 . .0225 


.022 


.56 


.025 


24 


25 


.02 


.0179 


.02 


.02 


.02 


.51 


.0219 


25 


26 


.018 


.01594 


.01 


8 .018 


.018 


.45 


.0188 


26 


27 


.016 


.01419 


.01 


7 .017 


.0164 


.42 


.0172 


27 


28 


.014 


.01264 


.01 


6 .016 


.0148 


.38 


.0156 


28 


29 


.013 


.01126 


.01 


5 .015 


.0136 


.35 


.0141 


29 


30 


.012 


.01002 


.01 


4 .014 


.0124 


.31 


.0125 


30 


31 


.01 


.00893 


.01 


35 .013 


.0116 


.29 


.0109 


31 


32 


.009 


.00795 


.01 


3 .012 


.0108 


.27 


.0101 


32 


33 


.008 


.00708 


,01 


1 .011 


.01 


.25 


.0094 


33 


34 


.007 


.0063 


.01 


.01 


.0092 


.23 


.0086 


34 


35 


.005 


.00561 


.00 


95 .0095 


.0084 


.21 


.0078 


35 


36 


.004 


.005 


.00 


9 .009 


.0076 


.19 


.007 


36 


37 




.00445 


.00 


85 .0085 


.0068 


.17 


.0066 


37 


38 




.00396 


.00 


8 .008 


.006 


.15 


.0063 


38 


39 




.00353 


.00 


75 .0075 


.0052 


.13 




39 


40 




.00314 


.00 


7 .007 


.0048 


.12 


«... 


40 


41 










.0044 


.11 




41 


42 






..! 




.004 


.10 




42 


43 






.«. 




.0036 


.09 




43 


44 










.0032 


.08 




44 


45 






... 




.0028 


.07 




45 


46 










.0024 


.06 


.•••• 


46 


47 






.!.* 




.002 


.05 




47 


48 










.0016 


.04 




48 


49 






..! 




.0012 


.03 




49 


50 










.001 


.025 




50 



IQi 



MISCELLANEOUS MATERIALS. — WIRE. 



Table 26. 



U. S. STANDARD GAUGE FOR SHEET AND PLATE IRON 
STEEL, 1893. 



AND 



o 

£c3 


eg'" <^ . 

•= ^ 5 « 
X a.2 = 


roximate 
ikness in 
ecimal 
•ts of an 
Inch. 


roximate 
ickness 

in 
liinetres. 


light per 
are Foot 
Ounces 
irdupois. 


ight per 
aie Foot 
Pounds 
irdupois. 


Ight per 
are Foot 
ilograms. 


light per 
are Metre 
ilograms. 


light per 
are Metre 
Pounds 
irdupois. 


^" 








.5^ 3 - c 


0. 3 „ 




m 




000(1000 


^ 


0.5 


12.7 


320 


20. 


9.072 


97.05 


215.28 


000000 


15/32 


0.46875 


11.90625 


300 


18.75 


8.505 


91.55 


201 .82 


00000 


7/16 


0.4375 


11.1125 


280 


17.5 


7.938 


85.44 


188.37 


0000 


13/32 


0.40625 


10.31875 


260 


16.25 


7.371 


79.33 


174.91 


000 


Vs 


0.375 


9.525 


240 


15. 


6.804 


73.24 


161.46 


GO 


11/32 


0.34375 


8.73125 


220 


13.75 


6.237 


67.13 


148.00 





5/16 


0.3125 


7.9375 


200 


12.5 


5.67 


61.03 


134.55 


1 


9/32 


0.28125 


7.14375 


180 


11.25 


5.103 


54.93 


121.09 


2 


17/64 


0.265625 


6.746875 


170 


10.625 


4.819 


51.88 


114.37 


3 


^ 


0.25 


6.35 


160 


10. 


4.536 


48.82 


107.64 


4 


15/64 


0.234375 


5.953125 


150 


9.375 


4.252 


45.77 


100.91 


5 


7/32 


0.21875 


5.55625 


140 


8.75 


3.969 


42.72 


94.18 


6 


13/64 


0.203125 


5.159375 


130 


8.125 


3.685 


39.67 


87.45 


7 


3/16 


0.1875 


4.7625 


120 


7.5 


3.402 


36.62 


80.72 


8 


11/64 


0.171875 


4.365625 


110 


6.875 


3.118 


33.57 


74.00 


9 


5/32 


0.15625 


3.96875 


100 


6.25 


2.835 


30.52 


67.27 


10 


9/64 


0.140625 


3.571875 


90 


5.625 


2.552 


27.46 


60.55 


11 


H 


0.125 


3.175 


80 


5. 


2.268 


24.41 


53.82 


12 


7/64 


0.109375 


2.778125 


70 


4.375 


1.984 


2^36 


47.09 


13 


3/32 


0.09375 


2.38125 


60 


3.75 


1.701 


18.31 


40.36 


14 


5/64 


0.078125 


1.984375 


50 


3.125 


1.417 


15.26 


33.64 


15 


9/128 


0.0703125 


1.7859375 


45 


2.8125 


1.276 


13.73 


30.27 


16 


1/16 


0.0625 


1.5875 


40 


2.5 


1.131 


12.21 


26.91 


17 


9/160 


0.05625 


1.42875 


36 


2.25 


1.021 


JO. 99 


24.22 


18 


1/20 


0.05 


1.27 


32 


2. 


0.9072 


9.765 


21.53 


19 


7/160 


0.04375 


1.11125 


28 


1.75 


0.7938 


8.544 


18.84 


20 


3/80 


0.0375 


0.9525 


24 


1.5 


0.6804 


7.324 


16.15 


21 


11/320 


0.034375 


0.873125 


22 


1.375 


0.6237 


6,713 


14.80 


22 


1/32 


0.03125 


0.793750 


20 


1.25 


0.567 


6.103 


13.46 


23 


9/320 


0.028125 


0.714375 


18 


1.125 


0.5103 


5.493 


12 11 


24 


1/40 


0.025 


0.635 


16 


1. 


0.4536 


4.882 


10.76 


25 


7/320 


0.021875 


0.555625 


14 


0.875 


0.3969 


4.272 


9.42 


26 


3/160 


0.01875 


0.47625 


12 


0.75 


0.3402 


3.662 


8.07 


27 


11/640 


0.0171875 


0.4365625 


11 


0.6875 


0.3119 


3.357 


7.40 


28 


1/64 


0.015625 


0.396875 


10 


0.625 


0.2835 


3.052 


6.73 


29 


9/640 


0.0140625 


0.3571875 


9 


0.5625 


0.2551 


2.746 


6.05 


30 


1/80 


0.0125 


0.3175 


8 


0.5 


0.2268 


2.441 


5.38 


31 


7/640 


0.0109375 


0.2778125 


7 


0.4375 


0.1984 


2.136 


4.71 


32 


13/1280 


0.01015625 


0.25796875 


61^ 


0.40625 


0.1843 


1.983 


4.37 


83 


3/320 


0.009375 


0.238125 


6 


0.375 


0.1701 


1.831 


4.04 


34 


11/1280 


0.00859375 


0.21828125 


^}4 


0.34375 


0.1559 


1.678 


3.70 


35 


5/640 


0.0078125 


0.1984375 


5 


0.3125 


0.1417 


1.526 


3.36 


36 


9/1280 


0.00703125 


0.17859375 


41^ 


0.28125 


0.1276 


1.373 


3.03 


37 


17/2560 


0.000640625 


0.168671875 


414 


0.265625 


0.1205 


1.297 


2.87 


38 


1/160 


0.00625 


0.15875 


4 


0.25 


0.1134 


1.221 


2.69 



MISCELLANEOUS MATERIALS. — WIRE. 



165 



Table 27. 
wire : iron, steel, and copper, 
weight of one foot in length. 



Diameters by the Birmingham 

Gauge for Iron Wire, Sheet Iron, 

and Steel. 


Diameter by Brown & Sharpe's 
Gauge. 


•si 


B 


Iron. 


Steel. 


Copper. 


^1 

6 eij 


1 


Iron. 


Steel. 


Copper. 










^O 


eg 

s 










In. 


Pound. 


Pound. 


Pound. 




In. 


Pound. 


Poimd. 


Pound. 


0000 


.454 


.540207 


.551360 


.623913 


0000 .46000 


.56074 


.566030 


.640513 


000 


.425 


.478656 


.483172 


.546752 


000 .40964 


.444683 


.448879 


.507916 


00 


• .380 


.3826tD0 


.386270 


.487099 


00 .36480 


.3.52659 


.355986 


.402830 





.340 


.306340 


.309:^30 


.349921 


.32486 


.279665 


282303 


.319451 


1 


.300 


.238500 


.240750 


.272430 


1 .28930 


.221786 


.223^'.)! 


.25:5342 


2 


.284 


.213738 


.315755 


.244146 


2 .25763 


.175888 


1775 IS 


.2001)11 


3 


.259 


.177765 


.179442 


.203054 


3 .22942 


.139480 


.i-lir'.)6 


.159:«3 


4 


.238 


.150107 


.151523 


.171461 


4.20431 


.110616 


.1 1 1i;gu 


.126353 


5 


.220 


.128260 


.129470 


.146507 


5 .18194 


.087720 


.( 88548 


.100200 


6 


.203 


.109204 


.110234 


.124740 


6 .16202 


.069565 


.070221 


.079462 


7 


.180 


.085860 


.086667 


.098075 


7 


.14428 


.05.5165 


.055685 


.0(;3013 


8 


.165 


.072146 


.072827 


.082410 


8 


.12849 


.043751 


.044164 


.049976 


9 


.148 


.058046 


.058593 


.066303 


9 


.11443 


.034699 


,035026 


(396:^6 


10 


.134 


.047583 


.048032 


.054353 


10 


.10189 


.027512 


.027772 


.031426 


11 


.120 


.038160 


.038520 


.043589 


11 


.090742 


.021820 


.022026 


.024924 


12 


.109 


.031485 


.031782 


.035964 


12 


.080808 


.017304 


.017468 


.019766 


13 


.095 


.023)16 


.024142 


.027319 


13 


.071961 


.013722 


.013851 


.015674 


14 


.083 


.018256 


.018428 


.020853 


14 


.064084 


.010886 


.010989 


.012435 


15 


.072 


.013738 


.013867 


.01.5693 


15 


.057068 


.008631 


.008712 


.009859 


16 


.065 


.011196 


.011302 


.012789 


161.050820 


.006845 


.006909 


.007819 


17 


.058 


.00'<915 


.008999 


.010183 


17 1.045257 


.005427 


.005478 


.006199 


18 


.049 


.0068t53 


.006423 


.007268 


181.040303 


.004304 


.004344 


.004916 


19 


.042 


.004675 


.004719 


.005340 


19.035890 


.003413 


.003445 


.003899 


20 


.035 


.003246 


.003277 


.003708 


20 .031961 


.002708 


.002734 


.003094 


21 


.032 


.00-^714 


.00J739 


.003100 


21 .028462 


.002147 


.002167 


.002452 


22 


.028 


.002078 


.002097 


.002373 


22.025347 


.001703 


.001719 


.001945 


23 


.025 


.001656 


.001672 


.001892 


23 .022571 


.001350 


.001363 


.001542 


24 


.022 


.001283 


.001295 


.001465 


241.020100 


.001071 


.001081 


.001,223 


25 


.020 


.001060 


.001070 


.001211 


251.017900 


.0008491 


.0008571 


.0009699 


26 


.018 


.00U8.)86 


.0008687 


.0009807 


26.015940 


.0006734 


.0006797 


.0007692 


27 


.016 


.0006784 


.0006848 


.0007749 


271.014195 


.0005340 


.00C5391 


.0006099 


28 


.014 


.0005194 


.0005243 


.0005933 


28' 012641 


.0004235 


.0004275 


.0004837 


29 


.013 


.0004479 


.0004.521 


.0005116 


29.011257 


.0003358 


.0002389 


.0003835 


30 


.012 


.0003816 


.0003852 


.00043.59 


30 .010025 


.0002663 


.0002688 


.0003042 


31 


.010 


.0002650 


.0002675 


.0003027 


31 .008928 


.0002113 


.0002132 


.0002413 


32 


.009 


.0002147 


.0002167 


.0002452 


32 .007950 


.0001675 


.0001691 


.0001913 


33 


.008 


.0001696 


.0001712 


.0001937 


33 .007080' .0001 328 


.0001341 


.0001517 


34 


.007 


.0001-^99 


.0001311 


.0001 4H3 


34 .006304' .0001 053 


.0001063 


.0001204 


35 


.005 


.000006i5 


.00006688 


.00007.568 


35 .005614 .00008366 


.00008145 


.0000956 


36 


.004 


.0000424 


.0000428 


.00004843 


36 .005000 .00001)625 


.0000(5687 


.0000757 


Sp. 


grav . . 


7.77 


7.85 


8.89 


37 .004453 .00005255 


.00005304 


.0000(5003 


Wts 


.of a 








38 .003965 '.00004 166 


.00004205 


.00004758 


Cub 


left... 


485. 


490. 


555. 


39 .003531 ' .00003305 


.0000: 33(5 


.00003775 


Cub 


icin... 


.2807 


.2836 


.3212 


40 .003144 .00002620 
1 1 


.00002644 


.00002992 



166 



MISCELLAXEorS MATERIALS. — WIRE. 



Table 28. 
SIZE AND WEIGHT OF IRON AND STEEL WIRE. 







si 

■1^ o 


P 


i 
IS 


gth of 1 Bun- 
e (63 lbs.) hi 
ards. 


rea of Section 
in DecinuUsof 1 
Square Inch. 


nal Breaking 
eight of Bright 
irket Wire in 
unds. 


sile Strength 
Bright Market 
ire per Square 
eh of Section 
PoundB. 


5C5 


5S 


iSi 


^.S^ 

^ 


■^.s 

^ 


^,^>^ 




i-o^^-H 


^ 


Q 


Eu 


J 


< 


< 


H 


OOOOO' .450 


1.863 


.5366 


2833.248 


39.12 


.15904 


12598 


78903 


0000 .400 


2.3.58 


.4240 


2238.878 


49.52 


.12566 


9955 


79326 


000 i .360 


2.911 


.3435 


1813.574 


61.13 


.10179 


8124 


79813 


ooi .a30 


3.465 


.2886 


1523.861 


72.77 


.08553 


6880 


80437 


.305 


4.057 


.2465 


1301.678 


85.20 


.073C6 


5926 


81110 


1 


.285 


4.645 


.2153 


1136.678 


97.55 


.00379 


5226 


81925 


2 


.265 


5.374 


.1861 


982.555 


112.85 


.0.5515 


4570 


82873 


3 


.245 


6.286 


.1591 


839.942 


132.01 


.04714 


3948 


83756 


4 


.225 


7.454 


.1342 


708.365 


156.53 


.03976 


3374 


84862 


5 


.205 


8.976 


.1114 


588.139 


188.50 


.03301 


2839 


86000 


6 


.190 


10.453 


.09566 


505.084 


219 51 


.02835 


2476 


87349 


7 


.175 


12.322 


.08115 


428.472 


2.5S.76 


.02405 


2136 


88802 


8 .160 


14.730 


.06786 


358.3008 


309.46 


.02011 


1813 


90153 


9, .145 


17.950 


.05571 


294.1488 


376.95 


.01651 


1507 


91276 


10 


.130 


22.333 


.04477 


236.4384 


468.99 


.01327 


1233 


92890 


11 


.1175 


27.340 


.03658 


193.1424 


574.14 


.01084 


1010 


93194 


12 


.105 


34.219 


.02922 


154.2816 


718.60 


.00866 


810 


93530 


13 


.0925 


44.092 


.02268 


119.7504 


925.93 


.00672 


631 


93917 


14 


.080 


58.916 


.01697 


89.6016 


1237.24 


.00503 


474 


94299 


151 .070 


76.984 


.01299 


68.5872 


1616.66 


.00385 


372 


96703 


16 .061 


101.488 


.00985 


52.008 


2131.25 


.00292 


292 


99922 


17| .0525 


137.174 


.00729 


38.4912 


2880.65 


.00216 


222 


102740 


18, .045 


186.335 


.00537 


28.3378 


3913.04 


.00159 


169 


106343 


19 .040 


235.084 




22.3872 


4936.70 


.0012566 


137 


109362 


20| .085 


308.079 




17.1389 


6469.66 


.0009621 


107 


111184 


21 


.031 


392.772 




13.4429 




.0007547 






22 


.028 


481.234 




10.9718 




.0006157 






23 


.025 


603.863 




8.7437 




.0004909 






24 


.0225 


745.710 




7.0805 




.0003976 






25 


.020 


943.396 




5.5968 




.0003142 






26 


.018 


1164.689 




4.5334 




.0002545 






27 


.017 


1305.670 




4.0439 




.0002270 






28 


.016 


1476.869 




3.5819 




.0002011 






29| .015 


1676.989 




3.1485 




.0001767 







30! OH 


1925.321 




2.7424 




.0001539 






31 1 .013 


2232.653 




2.3649 




.0001327 






32l .012 


2620.607 




2.0148 




.0001131 






.'33 .011 


3119.092 




1.6928 




.0000950 






34 .010 


3773 584 




1.3992 




.00007854 






35 


.0095 


4182.508 




1.2624 




.00007088 






36 


.009 


4657.728 




1.1336 




.00006362 






37 


.0085 


5222.035 




1.0111 




.00005675 






38 


.008 


5896.147 




.89549 




.00005027 






39 


.0075 


6724.291 




.78672 





.00004418 






40 


.007 


7698.253 




.68587 




.00003848 







The strengths given in the last column of the above table are based upon 
tests made with bright (not annealed) charcoal-iron wire. The strength of 
Swedish iron is abcmt 10 per cent less, and that of mild Bessemer and 
ordinary crucible cast steel about 10 and 25 percent respectively greater, 
than that <»f chnrcoal-iion. Special grades of crucible cast steel vary 
between 30 and 100 per ceiii over charoo-il-iion. Galvanizing reduces the 
tensile stiengtli by about 10 and annealin.: by about 25 per cent, while 
tinning and cumbering exert no iippart-nt influence upon the metal. 



MISCELLANEOUS MATERIALS. — WIRE. 



167 



Table 29. 

TENSILE STRENGTH OF WIRE. 

Pounds per Square Inch. 

German silver 81,735 to 92,224 

Bronze 78,049 

Brass (as drawn) 81,114 *' 98,578 

Copper'* ** 37,607'* 46,494 

Copper (annealed) 34,936 ** 45,210 

Iron 59,246** 97,908 

Steel 103,272 ** 318,823 



Table 30. 



NUMBER OF YARDS OF IRON WIRE TO THE BUNDLE. 



(Bundle weighs 63 lbs.) 



B. We 

Gauge. 

JSTo. 


. ards per 
Bundle. 
71 


B. w. 
Gauge. 

No. 11. 


** 1 

*' 2...... 


91 

105 


** 12 
" 13 


«' 3 


121 


** 14 


« 4 


143 


" 15 


« 5 


170 


'* 16 


•* 6 

" 7 

•' 8 


203 

239 

286 


" 17 
** 18 
** 19 


«* 9 


342 


** 20 


" 10 


420 





Yards per 
Bundle. 

, . 529 

.. 700 

.. 893 

.. 1142 

. . 1465 

.. 1954 

. . 2540 

.. 3150 

.. 4085 

.. 4912 



168 MISCELLANEOUS MATERIALS. — WIRE ROPES. 



Wire Ropes. 

Ordinary wire rope is composed of six strands, each containing 
seven or nineteen wires, laid up about a hemp or wire-strand 
centre, and is commonly known as " seven-wire '' or '* nineteen- 
wire rope/' as the case may be. 

Rope made with a hemp centre is more pliable than that which 
has a wire centre. 

For special purposes ropes of twelve, sixteen, or other num- 
bers of wire to the strand are made. 

Hawser-ropes are made of six strands, each of which is com- 
posed of twelve wires laid about a hemp centre. 

Wire ropes are made in several ways, according to the pur- 
poses for which they are to be used. Ordinary wire ropes are 
made with a long or short twist or ** lay "; the component strands 
are laid up into rope in a direction opposite to that in which the 
wires are laid into strands — that is, if the wires in the strands are 
laid from right to left the strands are laid into rope from left 
to right. In the Lang-lay or TJniter sal-lay rope the wires are 
laid into strands and the strauds into rope in the same direction — 
that is, if the wire is laid in the strands from right to left the 
strands are also laid into rope from right to left. In locked wire 
rope the wires of ihe exterior strands are drawn to such a shape 
that each one interlocks with its neighbor in such a way as to 
present a smooth cylindrical surface like a solid round bar. This 
style of rope cannot be spliced in the ordinary way ; joints are 
made by steel couplings of suitable form. 

Wire rope should not be coiled or uncoiled like hemp rope. 
Wiien it is wound upon a reel the reel should revolve on a 
spindle while the rope is paid oil ; when laid up in a coil, not on 
a reel, roll the coil on the ground like a wheel, and pay off the 
rope in that manner, so that there will be no danger of untwist- 
ing or ' kinking.*' 

To i)rescrve wire rope laid under ground or under water it is 
coaled with a mixture of mineral tar and fresh-slaked lime in 
Ihe proportion of one bushel of lime to one barrel of tar. The 
mixture is boiled and the rope saturated with it while hot; saw- 
dust is sometimes added to give the mixture body. Wire rope 
exposed to the weather is coated with raw linseed-oil, or with a 
paint comiwsed of equal parts of Spanish brown or lampblack 
wilb linseed oil 



MISCl:LLAKEOtjS MATERIALS. — WlU^ ROPES. 



169 



Table 31. 

STRENGTH OF IRON ROPES. 

HOISTING-KOPE, 6 STRANDS OF 19 WIRES EACH. 





Circum- 




Weight 
per Foot 


Breaking 


Proper 
Working 
Load iu 
Tons of 
2000 Lbs. 


Circum- 
ference 


Min. 
Size of 


Trade 


ference 


Diam- 


Rope 


Strain in 


of Hemp 


Drum 


No. 


m 


eter. 


Tons of 


Rope of 


or 




Inches. 




Hemp 

Centre. 


2000 Lbs. 


Equal 
Strength. 


Sheave 
in Feet. 


1 


6M 


2^ 


8.00 


74 


15 


153^ 


8 


2 


6 


2 


6.30 


65 


13 


143^ 


7 


3 


51^ 


m 


5.25 


54 


11 


13 


6^ 


4 


5 


1% 


4.10 


44 


9 


12 


5 


5 


4% 




3.65 


39 


8 


113^ 


m 


5^ 


4% 


1% 


3.00 


33 


61^ 


10^ 

9/^ 


4^ 


6 


4 


\}4 


2.50 


27 


^Yq 


4 


7 


31^ 


M 


2.00 


20 


4 


8 


33^ 


8 


33^ 




1.58 


16 


3 


7 


3 


9 


2^ 


% 


1.20 


111/^ 


21/^ 


6 


2% 


10 


2^ 


Ya 


0.88 


8.64 


^M 


5 


2}^ 


10^ 


2 


% 


0.60 


5.13 


134 


43^ 


2 


1% 


9/16 


0.48 


4.27 


1 


4 


IM 


lOM 




y2 


0.39 


3.48 


3^ 


1^ 


lOa 


^% 


7/16 


0.29 


3.00 


L^ 


3 


1^ 


10b 


134 


% 


0.23 


2.50 


% 


2^ 


1 






5/16 


0.16 


1.75 


5/16 


IM 


1 




M 


H 


0.09 


1.00 


3/16 


13^ 


M 



STANDING ROPE, 16 STRANDS OF 7 WIRES EACH. 



4% 


1^ 


3.37 


36 


9 


10% 




m 


]^ 


2.77 


30 


73^ 


10 




4 


134 


2.28 


25 


614 


9^ 




33^3 


1^/^ 


1 82 


20 


5 


8 




33^ 




1.50 


16 


4 


7 




2% 


% 


1.12 


12.3 


3 


5^^ 




2% 


M 


0.92 


9 


2^ 




21/^ 


11/16 


0.70 


7.6 


2 


5 




2 


% 


0.57 


5.8 


13^ 


4% 




1% 


9/16 


0.41 


4.1 


1 


4 




13^ 


.v^ 


0.31 


2.83 


M 


3^ 




m 


7/16 


0.23 


2.13 


^ 


2% 




1 3/16 


% 


0.21 


1.65 


23^ 




1 


5/16 


0.16 


1.38 


M 


2^ 




% 


9/32 


0.12 


1.03 


1/6 


1 





170 MISCELLAKEOUS MATERIALS. — WIRE ROPES. 
Table 33. 

STRENGTH OF STEEL ROPES. 

CAST STEEL HOISTING-ROPE WITH 6 STRANDS OF 19 WIRES 
EACH. 









Weight 


Breaking 


Proper 
Working 
Load in 


Circum- 
ference 


Min. 
Size of 


Trade 
No. 


Circum- 
ference. 


Diam- 
eter. 


per Foot 
in Lbs. 


Strain in 
Tons of 


of Hemp 
Rope of 


Di-um 
or 




Inches. 


Inches. 




2000 Lbs. 


2000 Lbs. 


Equal 
Strength. 


Sheave 
in Feet. 


1 


7 


2^ 


8.00 


155 


3? 




9 


2 


6M 


2l 


6.30 


125 


25 




8 


3 


53^ 




5.25 


106 


21 


15% 


'^V^ 


4 


5 


1% 


4.10 


86 


17 


6 


5 


4H 


1^ 


3.65 


77 


15 


13^ 


5^ 


5)4 


4}4 


1% 


3.00 


63 


12 


12^ 


5^ 


6 


4 


1/4 


2.50 


52 


10 


IIJ^ 


5 


7 


334 


1^ 


2.00 


42 


8 


10 


4^ 


8 


33^ 




1.58 


33 


6 


9^ 


4 


9 


2H 


% 


1 20 


25 


5 


8 


3M 


10 


2% 


% 


0.88 


18 


31^ 


6^ 


3V^ 


lOH 


2 




60 


14 


2}4 


5H 


3 


ioy> 


m 


9/16 


0.48 


9 


m 


4M 


2M 


10% 


iv^ 


^ 


0.39 


7H 




4V^ 


2 


lOa 


1% 


7/16 


0.29 


6 


\IA 


4 


19^ 


106 


'34 


% 


0.23 


^H 


% 


m 


1 7^ 




1 


5/16 


0.16 


3 


r* 


3 


IM 



STANDING ROPE FOR DERRICKS, ETC., WITH 6 STRANDS OF 7 
WIRES EACH. 



n 

12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 



m 


1^ 


3 37 


62 


13 


15 




4y4. 


1% 


2.77 


52 


11 


13 




4 


1^ 


2.28 


44 


9 


12 




^V2 


1^ 


1.82 


36 


7 


lOM 






1 


1.50 


30 


6 


10 




2M 


% 


1.12 


22 


4^ 


8f4 




2% 


% 


0.92 


17 




71^ 




23^ 


11/16 


0.70 


14 


2% 


61)^ 




2 


% 


0.57 


11 


2 


5V^ 




IM 


9/16 


0.41 


8 


n 


5 






^ 


0.31 


6 


1 




1% 


7/16 


0.23 


5 


1 




1 3/16 


H 


0.21 


4 






1 


5/16 


0.16 


3 


3^ 




V8 


9/32 


0.12 


2% 


H 





MISCELLANEOUS MATERIALS. — WIRE ROPES. 



171 



Table 33. 
STRENGTH OF GALVANIZED WIRE ROPES. 







73 


<_, 


•S^-^ 1 






CO 


r- 


rcumference of 
Hemp Rope of 
Equal Strength 
in Inches. 


£p5 




III 


oi 

05 _ 


rcumfereuce < 
Hemp Rope 
Equal Strengt 
in Inches. 


^.2 

•"do; 


0) 



a 

II 

Pa 


^ S 


ceo . 

¥1 


< 


5^ 


4.42 


« 


O 


< 


Q 


H 


« 





1.75 


43 


11 


0.80 


2)^ 


92 


81/^ 


5 


1.67 


5M 


4.08 


40 


101^ 


0.72 


214 


0.75 


7 


41^ 


1.60 


5 


3.67 


35 


10 


0.64 


2 


0.59 


6 


4 


1.51 


4% 
41^ 


3.50 


33 


93^ 


0.56 


m 


0.42 


5 


'S}4 


1.43 


3.17 


30 


9 


0.48 


m 


0.30 


31/^ 


3 


1.35 


4^ 


2.75 


26 


m 


0.40 


iH 


0.21 


2^ 


2J^ 


1 27 


4 


2.38 


23 


8 


0.36 


1^8 


0.17 


^H 


2H 


1.19 


3^ 


2.13 


20 


71^ 


0.32 


1 


0.14 


2 


2 


1.11 


3)^ 


1.79 


16 


7 


0.28 


% 


0.11 


1 


1^ 


1.04 


314 


1.58 


14 


Q}4 


0.24 


H 


0.085 


% 


IH 


96 


3 


1.33 


12 


6 


0.20 


0.06 


% 


1 


0.88 


2M 


1.13 


10 


5^ 


0.16 


« 


0.045 


M 


% 



Table 34. 

STRENGTH OF FLAT WIRE ROPES^ 







Breaking Strain 






Breaking Strain 




Approx- 


(Approximate) 




Approx- 


(Approximate) 


Size in 
Inches. 


imate 

Weight 

per Foot. 


in Pounds. 


Size in 
Inches. 


imate 

Weight 

per Foot. 


in Pounds. 












Pounds. 


Iron. 


Cast 
SteeL 




Pounds. 


Iron. 


Cast 
Steel. 


2 x% 


1.35 


20000 


40000 


3 x}4 


2.40 


37500 


75000 


m^Vs 


1.70 


25000 


50000 


3^x1^ 


2.85 


43750 


87500 


3 x% 


2.05 


30000 


60000 


4 xi^ 


3.30 


50000 


100000 


33^x% 


2.40 


35000 


70000 


5 x}4 


4.20 


62500 


125000 


4 x% 


2.75 


40000 


80000 


6 xYa 


5.10 


75000 


150000 


5 x% 


3.45 


50000 


100000 


7 y]4 


6.00 


87500 


175000 


6 x% 


4.15 


60000 


• 120000 


8 >c}4 


6.90 


100000 


200000 



For safe working load allow one fifth to one seventh of the breaking 
strain. 



It3 MiSCELLAKEOUS MATfiElALS.— WIRE ROP£S. 

Table 35. 
STRENGTH OF GALVANIZED STEEL CABLES. 



Cables laid up like Wire Rope. 


Cables composed of Wires laid 
Parallel and Bound Together. 


Diameter 
in Inches. 


Weight 
per Foot. 
Pounds. 


Ultimate 
Strength 
in Tons of 
2000 Lbs. 


Diameter 
in Inches. 


Weight 
per Foot. 
Pounds. 


Ultimate 
Strength 
in Tons of 
2000 Lbs. 


2% 
2^ 


11.7 
10.3 
9.2 
8.3 
6.5 
5.8 
5.6 
4.3 
3.7 


220 

200 

180 

155 

110 

100 

95 

75 

65 


4 

m 


35.26 
30.78 
26.23 
18.34 
15.40 
12.88 


760 
665 
580 
400 
325 
262 



Table 36. 

STRAIN ON HOISTING-CHAINS AND CABLES ON INCLINED 
PLANES. 



Rise per 

100 Feet 

Horizontal. 


Angle of 
Inclination. 


Strain in 

Lbs. per 

Ton of 

2000 Lbs. 


Rise per 

100 Feet 

Horizontal. 


Angle of 
Inclination. 


5 


2° 52' 


112 


105 


46° 24' 


10 


5 43 


211 


110 


47 44 


15 


8 32 


308 


115 


49 


20 


11 19 


404 


120 


50 12 


25 


14 3 


497 


125 


51 21 


30 


16 42 


585 


130 


52 26 


35 


19 18 


672 


135 


53 29 


40 


21 49 


754 


140 


54 28 


45 


24 14 


832 


1^5 


55 25 


50 


26 34 


905 


150 


56 19 


55 


28 49 


975 


155 


57 11 


60 


30 58 


1039 


160 


58 


65 


33 2 


1100 


165 


58 47 


70 


35 


1157 


170 


59 33 


75 


36 53 


1210 


175 


60 16 


80 


38 40 


1259 


180 


60 57 


85 


40 22 


1304 


185 


61 37 


90 


42 


1347 


190 


62 15 


95 


43 32 


1387 


195 


62 52 


100 


45 


1422 


200 


63 27 



Strain in 

Lbs. per 

Ton of 

2000 Lbs. 



1456 
1488 
1517 
1545 
1569 
1592 
1614 
1635 
1G54 
1671 
1687 
1702 
1716 
1730 
1743 
1754 
1766 
1776 
1785 
1794 



In calculating the strains on the chain an allowance of 12 lbs. per ton has 
been made for the rolling friction of the load on a level. An additional 
allowance should be made for thf^ weigrht of th^' chain, dependinsr of coiirpa 
on irssiz; and length. The breakini^ sir.iifi ..f -lie chain shouhl be six or 
seven tiint^s that which it is to beat . 



MISCELLANEOUS MATERIALS. — WIRE ROPES. 173 



Table 37. 

STRENGTH OF CRANE-CHAINS. 





' 


D. B. G 


." Special Crane. 






Crane. 






^ 


^ ^ 


W 




6C^ 


03 . 




!•§ 


"eS • 




1; 


§ 3 


^' 




-^ 9 


©-O 




^i 


2 CO 


g 


c8 


fe . a 


+2 




S 


'♦r^ 9 c 




<w a p 


g5 


^ll 
1^"^ 


|-§g 


!2 


IS 


Si 


eg <D r^ 

h ^ 


2^ 




C 03 ® 


cc 


S 


^ 


o 


^ 


< 





Q. 


< 





M 


25/32 


% 


% 


1932 


3864 


1288 


1680 


3360 


1120 


5/16 


27/32 


1 


1 1/16 


2898 


5796 


1932 


2520 


5040 


1680 


% 


31/32 


1 7/10 


ig 


4186 


6372 


2790 


3640 


7280 


2427 


7/16 


1 5/32 


2 


5796 


11592 


3864 


5040 


10080 


3360 


H 


1 11/32 


2^ 


1 11/16 


7728 


15456 


5182 


6720 


13440 


4480 


9/16 


1 15/32 


3 2/10 


m 


9660 


19320 


6440 


8400 


16800 


5600 


H 


1 28/32 


4^ 


2 1/16 


11914 


23828 


7942 


10360 


20720 


6907 


11/16 


1 27/32 


5 


2M 


14490 


28980 


9660 


12600 


25200 


8400 


13/16 


1 31/32 


5% 


21^ 


17388 


34776 


11592 


15120 


30240 


10080 


2 3/32 


6 7/10 


2 11/16 


20286 


40572 


13524 


17640 


35280 


11760 


Vs 


2 7/32 


8 


2% 


22484 


44968 


14989 


20440 


40880 


13627 


15/16 


2 15/32 


9 


3 1/16 


25872 


51744 


17248 


23520 


47040 


15680 


1 


2 19/32 


10 7/10 


3M 


29568 


59136 


19712 


26880 


53760 


17920 


1 1/16 


2 23/32 


11 2/10 


3 5/16 


33264 


66538 


22176 


30240 


60480 


20160 


m 


2 27/32 


121^ 


334 


37576 


75152 


25050 


34160 


68320 


22773 


1 3/16 


3 5/32 


13 7/10 


3% 


41888 


83776 


27925 


38080 


76160 


25387 


m 


3 7/32 


16 


4^ 


46200 


92400 


30800 


42000 


84000 


28000 


1 5/16 


3 15/32 


161^ 


4% 


50512 


101024 


33674 


45920 


91840 


30613 


Ws 


3% 


18 4/10 


4 9/16 


55748 


111496 


37165 


50680 


101360 


33787 


1 7/16 


3 25/32 


19 7/10 


4^ 


60368 


120736 


40245 


54880 


109760 


36587 




3 31/32 


21 7/10 


5 


66528 


133056 


44352 


60480 


120960 


40320 



The distance from centi-e of one link to centre of next is equal to the inside 
length of link, but in practice 1/32 inch is allowed for weld. This is approxi- 
mate, and where exactness is required chain should be made so. 

For Chain sheaves.— The diameter, if possible, should be not less than 
twenty times the diameter of chain used. Example : For 1-inch chain use 
20-inch sheaves. 



174 rASTENi:N gs.— nails. 



Vni. Fastenings. 
Nails. 

There is a large variety of nails, named chiefly from the shape 
of their heads or points, or according to the particular use for 
which they are intended. 

In former limes nails were described according to their price 
per 100; thus '* teupenny nails " and" fourpeuuy nails" were those 
costing tenpence and fourpence per 100 respectively. These 
terms are still used, but their meaning is indefinite or has refer- 
ence to nails of a particular length. 

Cast Nails, made by running iron into moulds, are brittle and 
inferior in strength. 

Wrought Nails are forged either by hand labor or machine 
power. They are frequently designated by the names clasp or 
clench nails, on account of their property of bearing bending with- 
out breaking. 

Cut Nails are made by machinery, of various thicknesses and 
in lengths from | to 6 inches. 

WiKE Nails are made by machinery. They are round or 
square in section and are smooth or barbed. They are made in 
lengths from | to 6 inches, and of different thickness, varying 
from Nos. 5 to 18 B. W. G. 

Copper Nails are made of the same shape as iron nails, and 
are used in positions where the latter would be subject to cor- 
rosion. 

Composition Nails are made of different alloys to avoid cor- 
rosion, or to prevent galvanic action set up by iron when in con- 
tact with zinc or other metals. They are varied in shape accord- 
ing to the purpose for which they are to be used. 

Holding Power of Nails. — In holding power cut nails are 
superior to wire nails. 

The main advantage of a wire nail is in its possessing a sharp 
point and in being easily driven. 

If cut nails were pointed their eflaciency in direct tension would 



FASTENINGS. — NATLS. 



175 



be iucreased by about dO%; wire nails without points have but 
half of their ordinary holding power. 

The tenacity of wire nails decreases with time, but not so fast, 
probably, when exposed to the weather. 

The nail's surface should be very slightly rough, though not 
granular ; should not be galvanized or otherwise made smooth; 
and should not be barbed, and especially the barbs should not be 
sharp and angular. Barbing decreases the eflaciency of cut nails 
about "62%. 

Nails to be used in tension should be about three times the 
thickness of the thinnest piece nailed in length, and when used 
in shear about twice the same. 

The relative holding power of nails in the common woods is 
about as follows : white pine 1 ; yellow pine 1.5 ; white oak 3 ; 
chestnut 1.6; beech 3.2; sycamore 2 ; elm 2; basswood 1.2; 
laurel 2.8. 

Nails usually hold about 60% more when driven perpendicular 
to the grain than when driven along the grain. 

When subject to impact nails hold less than y\ the strain they 
can stand when weight is gradually applied. 

Table 38. 

WROUGHT-IRON OR CLINCH NAILS. 
LENGTH AND NUMBER TO THE POUND. 



Title. 


Length. 


Number 
per Pound. 


Title. 


Length. 


Number 
per Pound. 


6d. 


2 in. 


95 


12d.- 


3J in. 


42 


7d. 


2i" 


74 


16d. 


4- 


38 


8d. 


2r* 


62 


20d. 


4 '* 


33 


9d. 


. 2I- 


53 


30d. 


4^-' 


20 


lOd. 


3 •' 


46 









176 



FASTENINGS. — NAILS. 



Table 39. 

CUT NAILS. 

LENGTH AND NUMBER TO THE POUND. 



Ordinary. 



Size. 



2d 

M fine 
3d 
4d 

M 

U 

Sd 
IM 
12d 
20d 
SOd 
40d 
60d 
60d 



4d 
M 



M 

lOri 
12(i 



Length, 
in inches. 



If 

2 

2i 

2i 

2^ 

3i 

3i 

4i 

41 

5 

5i 



No. to 
pound. 



716 

588 

448 

336 

216 

166 

118 

94 

72 

50 

32 

20 

17 

14 

10 



Light. 



1^ 
If 
2 



373 

272 
196 



Brads. 



2 

2i 
21 
3i 



163 
96 

74 
50 



Clinch. 



Length, 
in inches. 



2 

2i 

2i 

2i 

3 

3i 



No. to 
pound. 



152 

133 

92 

72 
60 
43 



Fence. 



2 

2i 

2i 

23 

3 



96 
66 
56 
50 
40 



Spikes. 



3i 
4 

4i 
5 

5i 



19 
15 
13 
10 

9 



Boat. 



206 



Finishing. 



4.d 

M 

M 
lOcZ 
12cZ 

2i)d 



Length, 
in inches. 



11 
If 

2 

2i 

3 

3^ 



Core. 



Cul 


2 


M 


2i 


\M 


2^ 


V2d 


3i 


20d 


3i 


nod 


4} 


40d 


4i 


WH 


2-.V 


^ V H L 


2i 



Slate. 



3(2 
4d 
5ri 
(yd 



13 

2 



Table 40. 

TACKS. 
SIZE AND NUMBER PER POUND. 





A* 


Number 




.c 


Number 






Number 


Size. 


a 


to 


Size. 




to 


Size. 


to 




^ 


pound. 




^ 


pound. 




3 


pound. 


1 OZ. 


* 


16000 


4 OZ. 


r',r 


4000 


14 OZ. 


ii 


1143 


H *^ 


i'b 


10066 


6 " 


"iHi 


2666 


16 " 


J 


1000 


2 " 


i 


8000 


8 '' 


ii 


2000 


18 " 


+1 


888 


2i *^ 


T^,T 


6400 


10 '' 


i,'i 


1600 


20 " 


1 


800 


3 " 


f 


5333 


12 '' 


1 


1333 


22 " 


ItV 


727 



FASTENINGS.— NAILS. 



177 



Table 41. 

WIRE NAILS. 
LENGTH AND NUMBER TO THE POUND. 







-d 








-d 




6i 














p 








(D 














CO 


e3 


o 










§e 






be 




6 


1 

(D 


03 

1 


a 
a 

o 
o 


o 




s 
I 

a 


6 


a-d 

iX) a 
ad'?: 

53 C3.-, 


CO 

1 

be 

a 

1 


fei) 


o 

0) 

u 


be 

c 


H 


hJ 


o 


m 


6 


fe 


02 


£ 


'J 


£ 


S 


PQ 


cc 




H 




















714 






Vs 




















469 


. • • • 


2d. 


1 


1200 


876' 


71*6* 




1558 


3550 


1350 




'ill 


411 




3d. 


ij^ 












1140 












3d. 


1/4 


720 


568' 


429" 




"980 




'913 




25 


251 




4d. 


1^ 


432 


357 


274 




760 


760 


584 




•-.'0( 


165 




5d. 


1% 


300 


235 


235 


142* 


575 




410 




141 


142 


270 


6d. 


2 


252 


204 


157 


124 


350 






310 


'157 




103 


204 


7d. 


2M 


186 


139 


139 


92 


275 


. . . 




238 


139 


18:- 






8d. 


2^ 


1S2 


99 


99 


82 


190 






170 


99 


125 






9d. 


2% 


105 


90 


90 


62 


173 






150 


90 


114 






lOd. 


3 


87 


69 


83 


50 


137 






121 


67 


83 






12d. 


m 


66 


53 


64 


38 


98 






97 


53 


.... 






16d. 


3>'2 


51 


43 


59 


30 


81 






72 


43 








20d. 


4 


35 


31 


43 


23 


71 






54 




. . . . 






30d. 


4)^ 


27 


24 


.... 










46 










40d. 


5 


21 


18 




.... 








36 










50d. 


51^ 


15 










. . . 




.... 










60d. 


6 


12 










... 















FASTENIKGS.— SPIKES. 



Table 42. 

WROUGHT SPIKES. 
SIZE AND NUMBEK IN KEG OF 150 POUNDS. 



Length 


J/4In. 


5/16 In. 


3/8 In. 


r/16 In. 


1/2 In. 


3 iu. 


2250 










3i" 


1890 


1208 








4 '' 


1650 


1135 


.... 






4i- 


1464 


1064 


• . • • 






5 * 


1380 


930 


742 






6 " 


1292 


868 


570 






7 '* 


1161 


662 


482 


445 


306 


8 '* 


* • • . 


635 


455 


384 


256 


9 " 


.... 


573 


424 


300 


240 


10 - 







391 


270 


222 


11 - 








249 


203 


12 »' 










236 


180 



Table 43. 

WIRE SPIKES. 
SIZE AND NUMBEK TO THE POUND. 



Title. 


No. of Wire. 


Length. 


No. per Pound. 


lOd. 


7 


3 in. 


50 


16d. 


6 


3i- 


35 


20(1. 


5 


4 '* 


26 


30d. 


4 


^" 


20 


40d. 


3 


5 *' 


15 


50d. 


2 


5^' 


12 


60d. 


X 


6 *' 


10 


6i in. 


1 


6i'' 


9 


7 " 





7 *' 


7 


8 " 


00 


8 •' 


5 


9 '' 


00 


9 *' 


H 



FASTENINGS. — SPIKES. 



179 



Table 44. 

TRACK-SPIKES. 
SIZE AND NUMBER PER KEG. 



Rails Used. 


Spikes. Inches. 


Number in Keg, 
200 Pounds. 


Kegs per Mile. 
Ties 24 Inches be- 
tween Centres. 


45 to 85 lbs. 


H X t\ 


380 


30 


40 '^ 52 '♦ 


5 Xf^ 


400 


27 


35 ** 40 '* 


5 X i 


490 


22 


24/' 35 '* 


4i X i 


550 


20 


24 ** 35 *' 


4i X A 


725 


15 


18 •' 24 *' 


4 XtV 


820 


18 


16 '* 20 *' 


Six f 


1250 


9 


14 '' 16 - 


3X1 


1350 


8 


8 " 12 " 


2^X f 


1550 


7 


8 - 10 '' 


^ X ft 


2200 


5 



Table 45. 

STREET-RAILWAY SPIKES. 
SIZE AND NUMBER PER KEG. 



Spikes. 
Inches. 



5 X I 

4| X A 



Number in Keg, 
200 Pounds. 



Kegs per Mile. Ties 24 I n 
between Centres. 



400 
575 

800 



30 
19 
13 



180 



FASTENINGS.— SCREWS. 



Screws. 

Screws for screwing into wood are made of metal with sharp 
or bevelled threads. The points are generally made sharp, so 
that they may penetrate the w^ood; the body of the screw is 
tapered, so that the deeper it is driven the more tightly it will 
fill the hole; the thread does not extend throughout the length 
of the screw, but a considerable portion below the head is left 
smooth. 

Screws are made in various lengths and diameters. They are 
classified according to the shape of their heads, and in some cases 
according to their use. The principal forms of the heads are the 
flat and the button or round head. The former are used when the 
thickness of the material is sufficient to permit the head of the 
screw being countersunk; the latter are used where the material 
is too thin to admit of countersinking, and also for ornamental 
. purposes. 

Screws to be used in damp places should be of brass. 

Table 46. 

DIMENSIONS OF WOOD SCREWS. 



No. 


Threads 
per Inch. 


Diameter 
of Body. 


Diameter 
of Flat 
Head. 


Diameter 

of Round 

Head. 


Diameter 

of 
FiHster 
Head. 


Lengths. 


Inches, 


From 


To 


2 


56 


.0842 


.1631 


.1544 


.1332 


3/16 


H 


3 


48 


.0973 


.1894 


.1786 


.1545 


3/16 


4 


32, 36, 40 


.1105 


.2158 


.2028 


.1747 


3/16 


1 


5 


32, 36. 40 


.1236 


.2421 


.2270 


.1985 


3/16 


6 


30, 32 


.1368 


.2684 


.2512 


.2175 


3/16 


1 


7 


30,32 


.1500 


.2947 


.2754 


.2392 


M 




8 


30,32 


.1631 


,3210 


.2936 


.2610 


H 


\IA 


9 


24, 30, 32 


.1763 


.3474 


.3238 


.2805 




1^ 


10 


24, 30, 32 


.1894 


.3737 


.3480 


.3035 


% 


JL^ 


12 


20,24 


.2158 


.4263 


.3922 


.3445 


IM 


14 


20,24 


.2421 


.4790 


.4364 


.3885 


s^ 


2 


16 


16, 18,20 


.2684 


.5316 


.4866 


.4300 


% 


2/4 


18 


16, 18 


.2947 


.5842 


.5248 


.4710 


1^ 


2V6 


20 


16, 18 


.3210 


.6368 


.5690 


.5200 


/^ 


23^ 


22 


16,18 


.3474 


.6894 


.6106 


.5557 


1^ 


3 


24 


14,16 


.3737 


.7420 


.6522 


.6005 


1^ 


3 


26 


14, 16 


.4000 


.7420 


.6938 


.6525 


^ 


3 


28 


14,16 


.4263 


.7946 


.7354 


.6920 


% 


3 


30 


14, 16 


.4520 


, .8473 


.7770 


.7240 


1 


3 



Lenprths vary by 16ths from 3/16 to 5^; by 8ths, from }^ to \}^\ by 4ths, 
from 1}^ to 3. 

Lag- or Coach-screws are large heavy screws used where 
great strength is required in heavy woodwork, and for fixing iron- 
work to timber. They have square heads, so that they can be 
screwed home with a wrench. 



FASTEKIKGS.— SCREWS. 



181 



Table 47. 

SIZE AND WEIGHT OF LAG-SCREWS. 
(The figures represent pounds per hundred.) 



Length. 


Diameter. Inches. 


Inches. 


Vs 


7/16 


V2 


V8 


M 


1% 

1% 

2 


6.88 

7.50 

8.25 

9.25 

9.62 

10.82 

11.50 

13.31 

14.82 

16.50 

17.37 

18.82 










11.75 
12.62 
12.88 
13.28 
16.62 
18.18 
18.88 
19.50 
21.25 
23.56 
25.31 


16.88 
17.18 
18.07 
19.18 
22.00 
24.00 
26.82 
28.25 
30.37 
33.88 
35.37 
38.94 
44.37 










2% 










34.07 
35.88 
39.25 
42.62 

47.75 
51.62 
55.12 
61.88 
68.75 
77.00 
90.00 




7 




64.00 
67.88 
71.37 
79.37 
86.62 
92.75 


8 






97.50 


9 






108.75 


10 








124.75 













Table 48. 

HOLDING POWER OF LAG-SCREWS. 

(Diameter of holes equal to diameter of the screw at the base of the 
thread ; depth of holes 1 inch less than the screw is to be sunk.) 



Wood. 


Diameter. Inches. 


1 


Vs 


M 


% 


^ 


7/16 


% 


5/16 


H 


Hemlock 


5150 
9270 
5410 
7050 
7760 


4730 
9040 
4710 
6240 
6740 


5090 
8350 
4380 
6860 
6690 


4840 
7410 
4350 
6410 
5980 


3130 
4300 
4670 
4560 
3730 


2660 
4030 
3900 
4060 
3240 


2100 
3120 
2020 
3410 
2930 


1790 
2400 
2110 
2470 
2250 


650 


Oak 


1400 


Pine, white 

'* Georgia 

•• Norway 


650 
1150 
1000 



1 82 FASTEN^INGS. — PINS — WEDGES. 

Screws for Metal are made in different forms from wood 
screws. The diameter of the screw is the same throughout. The 
threads are close together and V-shaped. 

The great difference between screws for metal and those for 
wood is that the latter, by the pressure of their threads against 
the fibres, make a hole into which they will fit exactly, whereas 
in metal the hole has to be tapped of the exact size to receive the 
screw. 

Unless the internal thread of the nut or of the metal into which 
the screw is to be driven exactly fits the thread of the screw one 
or the other will become distorted in screwing, they will bear un- 
equally upon one another, and great loss of strength will ensue, 
together with difficulties in working. 

Pins— Wedges. 

Pins are round pieces of iron or wood passed through the 
framing of a joint in timbers to prevent them from separating, or 
through a tenon to keep it from drawing out of the mortice. 

Trenails are pieces of hard wood used, like iron nails, for 
fastening boards to beams, for forming strong joints, etc., and 
occasionally, like pins, merely to secure joints formed in some 
other way. They are useful in positions where iron nails would 
rust and injure the work, and where copper nails would be too 
expensive. 

The}^ are made of different diameters and lengths according to 
the dimensions of the pieces they unite, and slightly tapering in 
form to facilitate driving. 

Wedges and Keys are made of hard wood inserted in a joint 
or between the sides of a tenon and the sides of a mortice. They 
are used for tightening up joints or forcing parts into position 
before inserting bolts, etc. They should be dipped in white lead 
before using. 



rASTEKIiTGS. — BOLTS AND NUTS. 183 



Bolts and Nuts, 

Bolts are manufactured either "rough" or ** finished." The 
finished bolt is the rough bolt turned to exact dimensions. 
Rough bolts are generally used for all woodwork. Finished bohs 
are only used in those cases where a close fit is absolutely essen' ial. 
Where they are used the holes for them must be drilled to an 
exact fit with the bolts. They are often used as a substitute for 
rivets. In cases where rivets would be subjected to direct tension 
tending to pull off the rivet-heads finished bolts are more reliable. 

Bolts are classed, first, according to the shape of the head, as 
round or button, square, liexagon, octagon , saucer ed, countersunk- 
headed, clinch, collared, chamfered, diamond, convex, etc. 

Second, by some structural peculiarity of the head, as eye, 
double-headed, hook, ring, "X -headed, etc. 

Third, by the mode of securing, as screw, fox, forelock, clinch^ 
rivet, ray, hay, barb, jag, key, etc. 

Fourth, by the nature and purpose of their application, as as- 
sembling, fish, foundation, anichor, drive, fender, lewis, set, shackle, 
king, scarf, etc. 

A Double-ended Bolt has a thread and nut on each end. 

A Flush Bolt is one whose head is let down even with the sur- 
face. 

A Foundation, Anchor, or Holding-down Bolt is a loag, 
heavy bolt holding machinery or a structure down to masonry. 
The hole is generally filled with sulphur, lead, or Portland 
cement. 

A Fox-bolt is one with a split end into which a wedge is 
driven. 

A HooK-BOLT is one with a hook head. 

A Key- BOLT is secured by a cotter or wedge passing through a 
slot in the shank. 

A Lewis-bolt is used for lifting large blocks of stone. 

A Ring-bolt is one which has an eye for receiving a ring. 

A Screw-bolt is one having a screw-thread on the whole or a 
considerable portion of its length. 

A Drift-pin is one used to expel another. Used also in rivet- 
ling to bring the holes fair for the entrance of the rivet. 

Drift-bolts are made both round and square. 

Round drift-bolts are superior to square bolts. 

Round drift-bolts should be driven in holes \l of their diame- 
ter, and square drift-bolts ] J of their width. 



184 



FASTENINGS. — BOLTS AND NUTS. 



Table 49. 

EFFECT OF DIAMETER OF HOLES ON HOLDING POWER OP 
DRIFT-BOLTS. 





Tenacity per 1 Inch Length in Wood. 


Diameter of 
Hole. 


Yellow Pine. 


White Oak. 




Round. 


Square. 


12/16 
13/16 
14/16 
15/16 


400 
788 
633 
375 


600 
675 

777 
710 


1133 
2499 

1778 
1301 



Washers are flat disks of iron placed under the nut of a bolt. 

The average relative holding power of drift-bolts, yellow pine 
being one, is in oak 3.1. 

The resistance to drawing a drift-bolt varies very nearly with 
the depth to which it is driven. 

Nuts must fit snugly, and the thread must pass through 
the nut and project at least one quarter of an inch. 

The heads and nuts must rest squarely upon the surface of the 
material which they unite. When the nuts or heads come against 
inclined surfaces bevelled washers of cast iron are used. 

The inspector must see that bolts of sufficient length are fur- 
nished and used. Cases are on record where bolts too short to 
pass through the nuts have been given a correct appearance by 
screwing threaded bolt-ends into the exposed sides of the nuts. 
Dummy bolts, that is, heads and screwed ends inserted in each side 
of the material to be joined, have been used to save both labor and 
material. Inspectors should keep a close watch for this practice. 



FASTENINGS. — BOLTS AND NUTS. 



185 



Table 50. 
STANDARD DIMENSIONS OF SCREWS, HEADS, AND NUTS. 





Short 


Short 


Long 


Long 


Thick- 


Thick- 


Thick- 


Diam. 


dlam. 
Bough. 


diam. 
Finish. 


diam. 
Rough. 


diameter 
Rough. 


ness. 

Rough 

Nut. 


ness 
Rough. 
Head. 


ness 
Finish. 
Both. 


of bolt. 


8 


^ 


^ 


<# 
















1 in 


W 












u 


1/4 


1/2 


7/16 


37/64 


7/10 


1/4 


1/4 


?/i^ 


5/16 


19/32 


17/33 


11/16 


10/12 


5/16 


19/64 


1/4 


3/8 


11/16 


5/8 


51/64 


63/64 


3/8 


11/32 


^Jl^ 


7/16 


25/33 


23/32 


9/10 


1ft 


7/16 


25/64 


3/8 


1/2 


7/8 


13/16 


1 


m 


1/2 


7/16 


7/16 


9/16 


31/32 


29/32 


li 


If* 


9/16 


31/64 


i/? 


5/8 


ItV 


1 


1ft 


H 


5/8 


17/32 


9/16 


3/4 


1? 


lA 


1ft 


Iff 


3/4 


5/8 


11/16 


7/8 


ItV 


IS 


1|J 


2ft 


7/8 


23/32 


13/16 


1 


li 


1t% 


If 


2il 


1 


13/16 


15/16 


n 


lit 


1 1 


2ft 


2ft 


H 


29/32 


1tJ« 


li 


2 


2ft 


2fi 


li 


1 


1ft 


11 


3A 


2^ 


Ol 7 
*32 


3ft 


If 


1ft 


1ft 


li 


21 


2ft 


2f 


3|| 


li 


1ft 


1\^ 


11 


2A 


3i 


2-i 


3f 


If 


1ft 


1ft 


]| 


2, 


2ii 




m 


If 


H 


IH 


ii 


2tI 


2f 


3il 


4ft 


1| 


I4f 


1« 


a 


3i 


3ft 


3f 


4|J 


2 


ift 


m 


2i 


3* 


3ft 


4ft 


4fJ 


2i 


li 


2ft 


2* 


3| 


3il 


41 


5|i 


2i 


HI 


2ft 


3| 


4J 


4ft 


4f| 


6 


2f 


2i 


m 


3 


4* 


4ft 


5f 


6H 


3 


2ft 


2H 


3i 


5 


4}| 


5H 


7ft 


3i 


2i 


3ft 


H 


51 


5ft 


6ft 


7|| 


3i 


m 


^'f 


3f 


5f 


5H 


6f4 


84 


31 


2| 


3il 


4 


H 


6ft 


7A 


8|i 


4 


3ft 


^ 


4i 


6i 


6ft 


7ft 


9ft 


4i 


3i 


4ft 


4i 


6J 


6il 


7»i 


9* 


4i 


3ft 


4ft 


4f 


7t 


7ft 


8rf 


lOi 


4f 


31 


m 


5 


71 


7ft 


8|| 


1011 


5 


3U 


4Tf 


5J 


8 




9ft 


11 il 


5i 


4 


5ft 


5i 


81 


8? 


9|f 


llf 


5i 


4ft 


5ft 


5| 


8f 


8U 


10ft 


12f 


5f 


4f 


^i 


6 


n 


SJft 


10^1 


121f 


6 


4ft 


6H 



186 FASTEKINGS. — BOLTS AND NUTS. 

Table 51. 

WEIGHT AND DIMENSIONS OF BOLTS AND NUTS. 



1 



Sij 


Size of Nut 


. 


Weight of Head and 
Nut or Two Nuts. 


Weight of 


5^ 












Bolt Bodies 












per Inch of 


P 


Width. 


Thick. 


Hole. 


Square. 


Hexagonal. 


Length. 


H 


^ 


M 


7/32 


.034 • 


.031 


.014 


5/16 


^ 


5/16 


9/32 


.067 


.055 


.021 


Vs 


^ 


% 


11/32 


.110 


.105 


.031 


7/16 


% 


7/16 


13/32 


.181 


.171 


.042 


^ 




^ 


7/16 


.280 


.233 


.055 


9/16 


11^ 


9/16 


5^ 


.369 


.335 


.069 


% 


11^ 


% 


9/16 


.545 


.475 


.085 


H 


1% 


% 


21/32 


.776 


.673 


.123 


% 


1^ 


% 


25/32 


1.34 


1.14 


.167 


1 


IM 




% 


1.75 


1.48 


.218 


Ws 


2 


13^ 


15/16 


2.47 




.276 


m 


2^ 


1J4 


1 1/16 


3.74 




.341 


1% 


2M 


1% 


1 3/16 


5.85 




.412 


w^ 


3 


1^ 


1 5/16 


7.59 





.491 


1^ 


314 


1% 


1 7/16 


9.48 




.576 


iM 


3K2 


IM 


1 9/16 


11.9 




.668 


1% 


Wa 


i^ 


1 11/16 


14.1 




.767 


2 


4 




1 13/16 


18.6 




.872 


2»^ 


4 


21/^ 


1 Vs 


18.9 




.985 


2M 


4 


214 


2 


19.3 





1.104 



In ordering bolts give the diameter, length under head, and length of 
thread required. 



FASTEKIKGS. — BOLTS AND NUTS. 



187 



Table 52. 

WEIGHT AND STRENGTH OF BOLTS. 



Ends Enlarged, or Upset. 


Ends Not 
Enlarged. 


Ends .Enlai-ged, or Upset. 


Ends Not 
Enlarged. 


CM . 


a« 




be 


'o^ 




o-^* 


u 


be 


• be 


^^i 


H 


s'l 




fl 


•§1 




5o 


6 ^ 


I5 




cui3 


3^ 


|2 


fi^ 




« 


S^ 


Q 


(U o 


Q 


o o 


W«^ 


w^ 


ft 


^& 


In. 


Lbs. 


Tons. 


Lbs. 


In. 


Lbs. 


In. 


Lbs. 


Tons. 


Lbs. 


In. 


Lbs. 


.%, 


.0414 
.093 


.245 
.553 


549 
1239 






13/16 


8.10 
8.69 


45.7 
49.0 


102368 
109760 


2.14 
2-22 


12.0 






12.9 


H 


.165 


.983 


2202 


.35 


.321 


Vs 


9.30 


52.5 


117600 


2.30 


13.8 


5/16 


.258 


1.53 


3427 


.43 


.452 


15/16 


9.93 


56.0 


125440 


2.38 


14.7 


% 


.372 


2.21 


4950 


.50 


.654 


2 


10.6 


59.7 


133728 


2.45 


15.7 


7/16 


.506 


3.00 


6720 


.58 


.897 


^ 


12.0 


63.8 


142912 


2.59 


17.5 


U 


.661 


3.93 


8803 


.66 


1.14 




13.4 


71.6 


160384 


2.73 


19.5 


9/16 


.837 


4.97 


11133 


.73 


1.41 


3^ 


14.9 


79.7 


178528 


2.88 


21.6 


% 


1.03 


6.14 


13754 


.80 


1.67 


% 


16.5 


88.4 


198016 


3.02 


23.9 


11/16 


1.25 


7.42 


16621 


.88 


2.03 


18.2 


97.4 


218176 


3.16 


26.1 


V, 


1.49 


8.83 


19779 


.96 


2.41 


M 


20.0 


106.9 


2394.56 


3.30 


28.5 


13/16 


1.75 


10.4 


23296 


1.04 


2.81 


Vh 


21.9 


116.8 


261632 


3.45 


31.1 


% 


2.03 


12.0 


26880 


1.12 


3.26 


3 


23.8 


127.2 


284928 


3.60 


33.9 


15/16 


2.33 


13.8 


30012 


1.20 


3.77 


H 


27.9 


141.0 


315840 


3.86 


39.1 


1 in. 


2.65 


15.7 


35168 


1.27 


4.27 




32.4 


163.6 


866464 


4.12 


44.4 


1/16 


2.99 


16.8 


37632 


1.35 


4.77 


% 


37.2 


187.7 


420448 


4.41 


51.0 


Vn 


8.35 


18.9 


42336 


1.42 


5.28 


4 


42.3 


213.6 


478464 


4.70 


57.8 


3/16 


3.73 


21.1 


47264 


1.49 


5.81 


H 


47.8 


227.0 


508480 


4.98 


65.2 


H 


4.13 


23.3 


52192 


1.55 


6.39 


Vo, 


53.6 


254.5 


570080 


5.25 


72.9 


5/16 


4.56 


25.7 


57568 


1.64 


7.04 


H 


59.7 


283.5 


635040 


5.53 


80.5 


% 5.00 


28.2 


63168 


1.72 


7.74 


5 


66.1 


314.2 


703808 


5.80 


88.1 


7/16 


5.47 


30.8 


68992* 1.80 


8.48 


M 


72.9 


824.7 


727328 


6.08 


97.0 


Vo 


5.95 


33.6 


75264 


1.87 


9.20 




80 


856.4 


798336 


6.86 


106. 


9/16 


6.46 


86.4 


81536 


1.94 


9.88 


H 


87.5 


389.5 


872480 


6.63 


116, 


% 


6.99 


39.4 


88256 


2.00 


10.6 


6 


95.2 


424.1 


949984 


6.90 


126. 


11/16 


7.53 


42.5 


95200 


2.07 


11.3 















Table 53. 

PLATE-IRON WASHERS. 



Diameters. 






Diameters. 










Thick- 
ness Bir- 
mingham 
Wire 

Gauge. 


Number 
of Wash- 
ers per 
Pound. 




Thick- 
ness Bir- 
mingham 
Wire 
Gauge. 


Number 


Washer. 
Inches. 


Bolt- 

hole. 

Inches. 


Washer 
Inches. 


Bolt- 
hole. 
Inches. 


of Wash- 
ers per 
Pound. 


14 


M 


18 


543 


m 


11/16 


10 


17. 


% 


5/16 


16 


228 


2 


13/16 


10 


10.7 


1 


5/16 


16 


147 


2yA 


15/16 


9 


8.7 


% 


16 


123 


1 1/16 


9 


6.8 


1 


7/16 


14 


70 


2% 




9 


4.7 


1^ 


^ 


14 


50 


3 


1% 


9 


3.7 


1% 


9/16 


12 


30 


3>^ 


]i^ 


9 


3.0 


1^ 


% 


12 


25.7 











188 FASTEKIN'GS. — RITETS- 



Rivets. 

Rivets are cylindrical pieces of metal with a solid Lead at one 
end, made of wrought iron, mild steel, or copper, eilher by hand 
or machinery. 

Iron and steel rivets are chiefly used to connect plates of iron 
and steel. They are preferable to small bolts, because, being 
hammered close to the face of the plate, they hold more tightly, 
and the shanks of rivets are not so likely to become oxidized as 
those of bolts; moreover, as rivets are nearly always fixed when 
hot, they contract in cooling and draw the plates together with 
great force. 

Size op Ri^tets. — The size of the rivet shown on the plans is 
the size of the cold rivet before heating. The diameter of the 
finished rivet should not be more than ^V i^ch greater than the 
cold rivet. The heated rivet should not drop into the hole, but 
should require a slight pressure to force it in. 

Rivets are described by the diameter and length in even eighths 
of an inch. 

The length of a rivet is determined by adding together the grip 
of the rivet, i. e. , the thickness of the plates or parts through which 
the rivet is to be driven, the length of metal required to form one 
head, and ^ of an inch for each joint between tlie plates to allow 
for uneven surfaces which prevent closer contact. The length 
thus found must be increased by about 9 per cent to allow for 
filling the rivet-hole, which is usually -^^ inch larger in diameter 
than the rivet; thus the length of rivet required to join three 
half-inch plates would be 2| inches. 

For countersunk heads add one half the diameter of the rivet 
for the head. 

The height of the head of a snap-rivet should be about | of the 
diameter of the shank, and the diameter of the head should be 
from 1^ to twice that of the shank. 



FASTENINGS.— RIVETS. 
Table 54. 

LENGTH OF RIVET-SHANK REQUIRED TO FORM HEAD. 



189 



Plain Rivets. 



t 


Diameter in Inches. 


A 




a 












.9 

i 


^ 


% 


H 


% 


1 




o 


Length in Inches. 



m 


1% 

1% 


1% 


2 


1% 


2 


2V^ 


1% 


2 


2V^ 




i% 


2^ 


2^ 


2% 


2 


2M 


23^ 


2^ 


''i% 






2% 


'iVA 


2V^ 


2% 


^% 


2% 


2^ 


2% 


2% 


2% 


3 


3^ 


all 


3 


3^ 


3I 


3V^ 


314 


3 


3H 


35^ 


3^ 


3^ 


s% 


31^ 


3% 


3H 




3^ 


3?| 




3% 


3^ 


3^ 


3^ 


3% 


4 


35^ 


3% 


4 


4^ 




4 


4^ 


4H 


3% 


4^ 


4H 
4«^ 


4% 


4 


4H 


4}^ 


4M 


4^ 


45/^ 


4% 


^% 


4^ 


4% 


4% 


4}/^ 


4% 


5 


4% 


4% 


5 


5^ 


4% 


5 


5^ 


1 


4% 


5^ 


5/4 


5 


53^ 


5% 


5% 


5^ 


5% 


5^ 


5^1 


51^ 


5% 


5% 


5% 


5% 


51^ 


5% 


5% 


6 


5% 


5% 


6 


6^ 


57^ 


61/^ 


6k 


6% 


6 


6U 


6^ 


6V^ 




61^ 


6% 


6H 


6^ 


6^ 


6% 


6% 


6% 


6% 

6% 


67^ 




6% 


7 


0% 


6% 


7 


7J^ 



21^ 
214 



2% 
2M 
2% 
3 

3^4 



4 

4^ 

4M 
4% 
41^ 



4% 
5 

5^ 
5M 



5% 
6 

6^ 
6^ 



6^ 

7 

7^ 

7^ 



Countersunk Rivets. 



^ 


Diameter in Inches. 


.a 




C 












a 


^ 


% 


H 


Vs 


1 


Oh 












*2 




Length in Inches. 



1 



1^ 

1% 

I'M 
1% 

2 

21^ 
214 



2^ 

m 

3 



334 
3% 

4 

4^ 



4% 



5^ 



1^ 
1^ 



1% 
2 

2^ 

2M 
2% 



2% 
2% 



3^ 
34 
33/^ 
3>^ 



3% 

4 

4^ 

44 
4% 
4^ 



4% 
5 

51/^ 



14 
1% 



1% 

2 

21^ 

24 
2% 
21/^ 
2% 

2M 

2% 



34 
3% 
3^ 



44 



m 



5 

54 



14 

II 

2 

2^ 

23/^ 

21^ 



2% 
3 

3M 

34 



3^ 
3% 
3% 



4 

4^ 

44 



4^ 



5 

5^ 
54 
5§2 



1^ 

1% 

5% 
2 

2^ 
24 



21^ 
2% 
2§4 

2% 



3^ 



4 

43^ 
44 



4^ 
4% 
4% 
4% 

5 

54 



5% 
5M 
5% 

6 
64 



190 FASTENINGS. — RIVETS. 

Form of Rivets. — There are various Dames given to rivets 
according to the shape to which the point is formed. 

Button or cap ended rivets are names given to rivet-heads formed 
with the " snap." 

Hammered rivets have points finished to a conical form by 
hammering only. 

Countersunk rivets are those in which the point is hammered 
down while hot flush with the surface of the plate. 

Pitch of Rivets. — The " pitch " of rivets is their distance 
from centre to centre. 

SiNGLE-RiYETiNG consists of a single row of rivets uniting 
plates in any form of joint. 

DouBLE-EiVETiNG Is that in which the plates are united by a 
double row of rivets. Double-riveting is designated as chain, 
staggered, or zigzag. Chain riveting is formed by parallel lines of 
rivets. Staggered or zigzag riveting consists of lines of rivets so 
placed that the rivets in each line divide the spaces between the 
rivets in the adjacent line or lines. 

Triple- and quadruple-TiYQlmg are formed by 3 or 4 rows of 
rivets, and may be either chain or staggered. 

The joints made in riveting are termed lap-joints when the 
plates overlap one another; fish- and butt joints when the ends 
of the pieces to be united meet or butt evenly against one 
another, the joint being made with a cover-plate on either one or 
both sides. 



FASTENIKGS. — RIVETS AND BOLTS, 



191 



Table 55. 

WEIGHT OF RIVETS AND ROUND-HEADED BOLTS WITHOUT 

NUTS PER 100. 

Length from under head. One cubic foot weighing 480 lbs. 



Length 




Diame 


iter of ri 


vet in inches. 


of rivet 










under 


















head. 


% 


V2 


% 


28.0 


Vs 


1 
64.6 


91.0 


IM 


li 


5.4 


12.5 


21.2 


42.5 


121.8 


l| 


5.9 


13.1 


22.4 


29.5 


44.6 


67.3 


94,5 


127.0 


H 


6.3 


13.7 


23.5 


31.0 


46.7 


69.9 


97.9 


132.4 


If 


6.7 


14.4 


24.7 


32.7 


48.9 


72.8 


101.2 


137.2 


If 


7.0 


15.1 


26.0 


34.2 


51.0 


75.0 


104.0 


141.1 


H 


7.3 


15,8 


27.1 


35.6 


53.3 


77.8 


107.3 


145.0 


2 


7.6 


16.5 


28.3 


37.0 


55.2 


81.3 


110.6 


149.2 


n 


7.9 


17.2 


29.6 


38.4 


57.5 


84.1 


113.9 


154.0 


sj 


8.3 


17.8 


31.0 


39.8 


59.5 


86.9 


118.2 


158.2 


2| 


8.8 


18.4 


32.1 


41.5 


61.7 


89.5 


122.1 


163,0 


2i 


9.1 


19.1 


33.2 


43.2 


63.9 


92.2 


125.5 


168.1 


2f 


9.5 


19.8 


34.4 


44.8 


66.0 


94.8 


129.0 


172. a 


2f 


9.8 


20.5 


35.4 


46.1 


68.2 


97.3 


132.4 


176.(1 


2| 


10.2 


21.2 


36.1 


47.7 


70.1 


100.0 


135.9 


180.3: 


3^ 


10.6 


21.9 


37.0 


49.0 


72.1 


102.5 


139.4 


184.9 


^ 


11.0 


22.7 


38.2 


50.6 


74.0 


105.1 


142.5 


189.01 


4 


11.3 


23.4 


39.1 


52.1 


76.2 


107.8 


146.1 


194. E 


3f 


11.7 


24.0 


40.2 


53.7 


78.5 


110.4 


149.6 


198. r 


3i 


12.1 


24.7 


41.0 


55.2 


80.2 


112.9 


153 


202.0 


3f 


12.5 


25.3 


42.0 


56.7 


82.4 


115.5 


156.5 


206.1 


3f 


12.8 


26.0 


42.9 


58.1 


84.3 


118.0 


160.1 


210.2 


3| 


13.2 


26.6 


44.1 


60.0 


86.5 


120.6 


163.4 


214.1 


4 


13.6 


27.2 


45.1 


61.5 


88.7 


123.2 


166.9 


218.0 


4i 


14.0 


28.0 


46.2 


63.2 


91.0 


125.7 


170.2 


221.9 


4 


14.4 


28.9 


47.1 


65.1 


93.4 


128.3 


173.6 


225.8 


41 


14.9 


29.5 


48.0 


66.6 


95.1 


131.0 


176.9 


229.5 


4* 


15.3 


30.2 


48.9 


68.0 


97.3 


133.6 


180.3 


234.9 


4f 


15.7 


30.9 


49.8 


69.2 


99.5 


136.2 


183.8 


239.0 


41 


16.1 


31.6 


51.0 


70.9 


101.1 


138.8 


187.2 


244.0 


4| 


16.5 


32.2 


52,1 


72.5 


103.4 


141.3 


191.0 


248.2 


5 


17.0 


32.9 


53.3 


74.2 


105.2 


144.0 


194.5 


252.1 


5i 


17.6 


33.9 


55.6 


77.2 


109.8 


150.0 


201.3 


260.9 


5^ 


18.2 


35.1 


56.8 


80.3 


114.1 


155.7 


208.1 


269.7 


5f 


18.9 


36.6 


58.0 


83.2 


118.0 


161.0 


214.9 


278.3 


6 


19.7 


37.7 


59.9 


86.1 


122.7 


166.1 


222.0 


287.1 


7 


22.3 


42.8 


67.0 


98.4 


141.1 


188.0 


250.0 


319.0 


8 


24.7 


48.0 


76.1 


112.2 


157.9 


213.0 


278.1 


353.4 


9 


27.4 


53.9 


83.9 


124.0 


172 5 


234.0 


304 9 


388.4 


10 


31.0 


59.0 


90.8 


135.9 


188.1 


1 254.3 


332.1 


421.0 


12 


37.7 


70.9 


108.4 


160.0 


221.5 


298.3 


387.9 


490.0 



For length of shank required to form rivet-head see Table 51. 



192 



FASTENINGS. — RIVETS. 



Field-rivets are those driven in a structure after it is in 
place. Wrought iron is generally used for field-rivets, because it 
is less liable to injury from overheating and from the decrease 
in temperature due to the loss of time in passing from the forge 
to the riveters. Steel properly heated would cool to a point below 
which it is not advisable to do any work upon it, and if heated 
to a temperature sufficient to compensate for the cooling it would 
be subjected to such oxidation as would make it ** red-short." 

Conventional Rivet-signs. — The size and location of rivets 
are usually marked on the working drawings in figures, but the 
form of the head, as well as whether they are to be driven in the 
shop or field, are indicated by conventional signs as shown by the 
following figures: 



Shop-Rivets *k Field-Rivets J 

-Countersunk — >|< ^Flattened — >K Plain->H Coiintersnnk Jj 




^0m'^0'$'t$$ 




C0>fVENTI0NAL RiVET-SIGNS. 

Riveting. — The process of riveting is performed either by 
hand or by machines, operated by air-, steam-, or water-power. In 
either method it consists of heating the rivet, passing it through 
the holes in the pieces to be united while hot, and then forging 
another head out of the projecting shank. 

Hand-ki\^ting. — In hand-riveting the forging is performed 
with hammers having flat faces. The end of the shank is upset 
and hammered until it forms a convex point. This is generally 
finished with a tool called a "snap," which is hollowed out to 
form a cup that will fit the point of the rivet. A heavy sledge- 
hammer called a "cupping "-hammer is used to strike the snap. 
The snap is generally used just as the rivet is losing its red heat. 
During the forging the rivet is held in place by an iron bar or 
••dolly," one end of which is hollowed out in the form of a cup 
that fits on the head of the rivet. " Spring "-dollies should be 
used where possible, especially for heavy pieces. For light work 
simple hand-dollies weighing from 15 to 25 pounds are used. 
The man who holds the dolly is called the " holder up." 



FASTENINGS. — RIVETS. 193 

Machine-riveting is cheaper and superior to hand-riveting. 
The steady pressure brought by the machine upon the rivet not 
only forms the head, but compresses and enlarges the shank, so 
that it is squeezed into and thoroughly fills up all the irregulari- 
ties of the holes. The superiority of machine- riveting is strik- 
ingly shown when rivets have to be taken out. After the head 
is cut off a hand-forged rivet may be easily driven out, but a 
machine-driven rivet must, as a rule, be drilled out. 

Machine-driven rivets can generally be easily distinguished 
from those formed by hand; the latter are covered with marks 
caused by the hammer and shifting of the snap during the forg- 
ing, while on a machine-riveted head there is generally a burr, 
caused by the die having caught the rivet a little out of the 
centre. 

Pressure required for Riveting. — It has been found in 
girder-work that for red-hot rivets of iron or soft steel, with 
length of grip not exceeding three diameters, a pressure of 50 
tons per square inch of rivet-section has been suflScient to com- 
pletely fill the hole. Longer rivets require higher pressure, and 
in extreme cases this pressure may be doubled to secure solidity. 

For cold-riveting the pressure required is about 300,000 lbs. 
per square inch of rivet-section. 

The pressures usually employed are as follows ; 



Inches: % 


H 


% 


1 


m 


m 


Tons: 25 


33 


50 


66 


75 


100 



Calking is a process adopted when it is found that the rivets 
are loose, or that the head or point of the rivet is not quite close 
to the plates, or that an opening exists between the plates them- 
selves. The process consists in hammering down the edges of 
the head or point of the rivets until they indent and slightly 
penetrate the surface of the plates. 

Cold riveting. — Very small iron and copper rivets are closed 
cold The iron used must be of the best quality. 



194 FASTENINGS.— RIVETS. 



Inspection of Riveting, 

TasTS FOR Rivet-metal. — The requirements of specifications 
vary considerably in regard to the properties of rivet-metal; a 
usual specification is as follows: 

** Steel for rivets shall have, in test-pieces f inch in diameter, 
an ultimate tensile strength of from 48,000 to 50,000 pounds per 
square inch; an elongation in 8 inches of 2Q per cent. 

** Heated uniformly to a light yellow and cooled in water at 
82° F., it shall bend round a circle of diameter equal to one and 
a half times the thickness of the specimen without fracture. 

" Full-size rivet-bars shall bend cold and double flat on them- 
selves without sign of fracture on the convex side." 

U. S. Navy Department Test.— From each lot (ton) twelvj 
rivets are to be taken at random and submitted to the followic^; 
tests: Four rivets to be flattened out cold under the hammer lo 
a thickness of one half the diameter without showing cracks oi 
flaws. Four rivets to be flattened out hot under the hammer to 
a thickness of one third the diameter v/ithout showing cracks or 
flaws; the heat to be the working heat when driven. Four rivets 
to be bent cold into the form of a hook with parallel sides with- 
out showing cracks or flaws. 

Iron for rivets must be tough and soft, and specimens of the 
full diameter of the rivet must be capable of bending cold until 
the sides are in close contact without sign of fracture on the con- 
vex side of the curve. 

A rivet of good iron when cut out of the work with a cold- 
chisel and hammer sliould show tough and fibrous and should not 
•* fly "; if it does it indicates brittleness. 

Essentials of Good Riveting. — Rivet-holes, — The holes in 
material to be riveted are either punched or drilled. 

In whichever way they are formed it is Important that they 
should be cut clean and true, and should fit exactly over one 
another. If they do not, irregularities are formed, which have to 
be forcibly removed by driving a steel ''drift-pin" into them 
before inserting the rivet, thus injuring the material, enlarging 
the hole, and causing the rivet to fit loosely. 

In punching holes examine the punches and dies and see that 
they are sharp and in perfect condition; good metal may be badly 
damaL^ed by the use of imperfect punches and dies. 

Holes should be punched from the side of the material that 



FASTENINGS. — RIVETS. 195 

will be exposed in the work; that is, the bevel of the hole must be 
away from the surfaces that are to be in contact. 

It is the current practice to punch the holes ^^ inch larger than 
the rivet diameter. For work to be reamed it is usual to punch 
the holes from | to j\ inch smaller than the finished diameter, 
the holes being reamed to the proper size after the various parts 
are assembled. 

The sharp edges or burr on the sides of the holes should be re- 
moved so as to form a fillet at the junction of the body and head 
of the finished rivet. 

After reaming the hole should be entirely smooth, showing 
that the reaming tool has everywhere touched the metal. 

Heating Rivets. — The heating of rivets requires Avatching to 
prevent burning. There is no way of telling after a rivet has been 
driven whether ii is burned, for the head may look perfectly good 
while the shank is badly damaged. 

The burning of rivets is not always accidental ; often if the 
rivet is so long as to more than fill the snap the heater will 
*' waste " the end, that is to say, he will burn it so badly that it 
will crumble off 

Steel rivets require careful handling to prevent overheating and 
to avoid working them at too low a heat, or at what is called a 
*' blue heat " They should be heated uniformly to a dull-red heat 
and the orange color should not be passed ; they should be placed 
in the work immediately the proper temperature is reached and 
the head forj^ed as rapidly as possible. 

Jron rivets can be heated to the *' waste " or '* wash'* heat, a 
temperature at which the intermingled slag in the metal begins 
to soak out from it without serious injury. Iron rivets should not 
be worked at a blue heat. 

Iron rivets should not be raised above a dull red (by daylight), 
and should not be twice heated. Burned rivets are weak and 
brittle. A large number of rivets should not be put into the fire 
at once to save trouble: they are liable to be left too long and con- 
sequently burned. 

For riveting by hand it is desirable that the head of the rivet 
should be eveu hotter than the point; otherwise the blows which 
are sufficient to expand the rivet and make it fill the hole near the 
point will not have much effect at the other end, and the rivet 
will not quite fill the hole near the head. 

The forge in which the rivets are heated should be placed as 
close to the point of use as possible. 



196 FASTENINGS. — RIVETS. 

The two heads must be concentric, fit closely all around, and 
no impress on the metal around the head should be made in driv- 
ing. The finished rivet-head should be without cracks. 

Redriving cold rivets and calking of rivet -heads should not be 
permitted. 

IjQose Rivets are detected by striking the rivet a sharp blow 
on each side of the head with a hammer weighing about or 
pound, the handle to which should be quite small in the shan( 
so as to allow the absorption at this point of some of the spring o 
the hammer. When the handle is held at the proper point and 
the rivets are solid no jarring effect is felt in the hand. Practice 
soon enables one to detect loose rivets by means of the action of 
the handle where no rattling sound can be heard, and where no 
movement could be detected by the finger placed at the angle be- 
tween the rivet-head and the web. 

Loose rivets are frequently made to appear tight by going 
round the edges with a calking-tool. They will feel and 
sound all right and the marks of the calking-tool will not be 
noticed unless it is especially looked for. Loose rivets are also 
tightened by placing the "snap" sideways upon the rivet and 
striking it two*or three blows with a sledge. It will then ap- 
pear to be tight, partly because it is bent and partly because 
the snap cuts a ridge in the plate and forces the metal against 
the head. Rivets tightened in this way show this ridge below 
the head, but a similar mark will often be made in shaping 
the head of a perfectly tight rivet, so the inspector cannot con- 
demn work simply because this mark appears, but such work 
should be regarded with suspicion, and a sharp watch kept upon 
the workman. It will also be advisable to have a few of the sus- 
picious rivets cut out. 

The ' ' held-up " head should be closely examined ; a rivet may 
be perfectly tight on the head, while in consequence of poor heat- 
ing it may be readily moved on the ** held-up" side. Besides, the 
riveter cannot tamper with that part of the rivet, and any marks 
there will show that he has been trying to conceal bad work. 

Very often there is trouble with countersunk rivets driven by 
a machine. The reason is this : the rivets are a trifle too long. 
This excess material spreads out under the die and overlaps the 
hole. Being thin this edge hardens quickly, and then no amount 
of pressure will upset the body of the rivet any further. It will 
appear tight until chipped, when it is often found to be loose. 

Drawings often require flat- head rivets in certain places where 



FASTENINGS. — RIVETS. 197 

there is not enough clearance foi^ the hemispherical head, and yet 
where all the space obtained by countersinking is not necessary 
Ou account of the ditticulty mentioned above such rivet-heads 
less than J inch in thickness should not be allowed. If left un- 
chipped it cannot be known whether the rivet fills the hole or 
not. 

Marking Rivets to be Cut Out.— In marking rivets to be 
cut out the inspector should use a centre-punch or the stamping 
end of his hammer with which to mark the head of the rivet, 
which should then be painted with white paint. A mark should 
also be made on the material near the rivet, so that he may be able 
to find aad test the new rivet. 



CHAPTER III. 

CONSTRUCTION. 

I. Earthwork. 

Definitions of Earthwork. 

The term "earthwork" is applied to all the operations per- 
formed in the making of excavations and embankments. In its 
widest sense it comprehends work in rock as well as in the 
looser materials of the earth's crust. 

Classification of Earthwork. — Excavation is usually 
classified under the heads Earth, Hardpan, Loose Rocky and Solid 
Rock, For each of these classes a specific price is usually agreed 
upon, and an extra allowance is sometimes made when the haul 
or distance to which the excavated material is moved exceeds a 
given amount. 

The characteristics which determine the class to which a given 
material belongs are usually described with clearness in the 
specifications, as: 

Earth will include loam, clay, sand, and loose gravel. 

Hardpan will include cemented gravel, slate, cobbles, and 
boulders containing less than one cubic foot, and all other mat- 
ters of an earthy nature, however compact they may be. 

Loose Rock will include shale, decomposed rock, boulders, and 
detached masses of rock containing not less than three cubic 
feet, and all other matters of a rock nature which may be loosened 
with the pick, although blasting may be resorted to in order to 
expedite the work. 

Solid Rock will include all rock found in place in ledges and 
masses or boulders measuring more than three cubic feet, and 
which can only be removed by blasting. 

Prosecution of Earthwork.— No general rule can be laid 
down for the exact method of carrying on an excavation and dis- 
posing of the excavated material. The operation in each case 
can only be determined by the requirements of the contract, 
character of the material, magnitude of the work, length of 
haul, etc. 

Duty of Inspector.— The duty of the inspector of earthwork 
is to see that the excavations are made to the depths and widths 

198 



EARTHWORK.— DEFINITIONS OF EARTHWORK. 199 



marked on the plans or directed by the engineer; that the sides 
of excavations, when required, are properly sheathed and braced 
so as to prevent slips and. to afford protection to the workmen; 
that the excavated material is deposited in the manner pre- 
scribed by the specifications and within the lines and with the 
slopes indicated by the plans, etc. 

The inspector should keep a record of the number of men and 
vehicles employed. On some works he will be required to 
determine the class to which the excavated material belongs, and 
sometimes its amount. 

Slopes of Earthwork. — The sides of excavations and em- 
bankments are finished with slopes corresponding to the angle of 
repose of the material ; that is, the angle at which the friction 
among the particles is sufficient to resist motion. 

The angles of repose for different earths are given in Table 56. 
But for all practical purposes it may be said that all earths, sand, 
and gravel stand at a slope of 83 degrees 41 minutes, or 1^ to 1. 
Rock is finished either vertical or at a slope of ^ to 1, 

Table 56. 

NATURAL SLOPES OF EARTHS (WITH HORIZONTAL LINE), 

Gravel (average) 40 degress 

Dry sand 38 

Wet *' 22 

Vegetable earth 28 " 

Compact earth 50 ** 

Shingle 39 '* 

Rubble 45 

Clay (well drained) 45 ** 

** (wet) 16 

Table 57. 

LENGTHS AND ANGLES OF SLOPES. 





Angl^ 


Length. 




Angle 


Length. 


Slope. 


with 


(Height taken 


Slope. 


with 


(Height takeu 




Horizon. 


as 1.00.) 




Horizon. 


as 1.00.; 


i-l 


75" 58' 


1.0307 


U:l 


33° 41' 


1.802 


i:l 


63 26 


1.118 


n 


1 


20 44 


2.016 


f.l 


53 8 


1.25 


2 


1 


26 34 


2.236 


1 : 1 


45 


1.4142 


3 


1 


18 26 


3.162 


Ij.l 


38 40 


1.6 


4 


1 


14 2 


4.124 



200 EARTHWORK. — DEFINITIONS OF EARTHWORK. 

The sides of an excavation will stand for a short time with a 
vertical face for a certain depth below its upper edge. That 
depth is greater the greater the adhesion of the earth as com- 
pared with its heaviness; the adhesion is increased by a moderate 
degree of moisture, but diminished by excessive wetness. 

The approximate depth at which earths will thus stand are as 

to Hows: 

tj>^^4.u Greatest Depth of 

^^"°' Tern. Vert. Face. 

Clean dry sand and gravel from to 1 foot 

Moist sand and ordinary surface-mould . *' 3**6 feet 

Clay (ordinary) ** 10 '^ 16 ** 

Compact gravel, .......** 10 ** 15 ** 

Form of Side Slopes. — The natural, strongest, and ultimate 
form of earth slopes is a concave curve in which the flattest por- 
tion is at the bottom. Ti^is form is very rarely given to the slopes 
in constructing them; in fact, the reverse is often the case, the 
slopes being made convex, thus saving excavation for the con- 
tractor and inviting slips^ 

In cuttings exceeding 10 feet in depth the forming of concave 
slopes will materially aid in preventing slipi, and in any case 
they will reduce the amount of material which will eventually 
have to be removed when cleaning up. Straight or convex slopes 
will continue to slip until the natural form is attained. 

Increase and Shrinkage of Excavated Material. 

All materials when excavated increase in bulk, but after being 
deposited in banks subside or shrink (rock excepted) until they 
occupy less space than in the pit from which excavated. 

The shrinkage of the different materials is about as follows : 

Gravel 8 per cent 

Gravel and sand 9 * * 

Clay and clay earths 10 *' 

Loam and light sandy earths 12 '* 

Loose vegetable soil 15 ** 

Puddled clay 25 ** 

Rock; on the other hand, increases in volume by being broken 
up, and does not settle again into less than its original bulk. The 
increase may be taken at 50 per cent. 

Thus an excavation of loam measuring 1000 cubic yards will 
form only about 880 cubic yards of enibanknieut, or an embank- 



I 



E^KXHWORK— EXCAVATXOK. 201 

meut of 1000 cubic j^ards wi]l require about 1120 cubic yards 
measured la excavation to make it. A rock excavation measuring 
1000 yards will make from 1500 to 1700 cubic yards of embank- 
ment, depending upon the size of the fragments. 

The lineal settlement of earth embankments will be about in 
the ratio given above; therefore either the contractor should be 
instructed in setting his poles to guide him as to the height of 
grade on an earth embankment to add the required percentage to 
the fill marked on the stakes, or the percentage may be included 
in the fill marked on the stakes. In rock embankments this is 
not necessary. 

Excavation. 

The prosecution of an excavation comprises the "loosening** 
of the compact earth and its removal. 

Loosening Earth. — The loosening is effected in such materials 
as sand and loose gravel, soft earth and loam, by ploughs if the 
area is of sufficient extent; if in trenches by the shovel alone. The 
stiffer earths and soft rocks are loosened with picks, crowbars, 
and wedges, the harder earths and solid rock by blasting. Ex- 
cavation of soft material under water is performed by machines 
called dredges. Rock under water is removed by blasting and 
dredging. 

The rapidity with which an excavation can be made depends 
upon the difficulty of getting out the earth. 

With hard clay, requiring two picks to a shovel, and with a 
small surface to work upon, two carts upon an ordinary road will 
take away all that a dozen men can get out; while with an easy 
soil, where one pick will keep half a dozen shovels busy, a 
larger number of vehicles will be required, or a quicker haul, 
which may be obtained by putting down a track. The less the 
haul, or the greater the speed of transport, the fewer may be the 
number of vehicles to remove a given amount of material. The 
chief point to be gained is to arrange the different classes of 
laborers so that none shall be kept waiting. Everything depends 
upon the tact for management possessed by the overseer. 

The amount of ordinary earth loosened by a plough and team 
of horses is from 20 to 40 cubic yards per hour. 

By the pick per man : 

Clay or cemented gravel. ... 1 yard per hour 

Loam and loose gravel 2 to 3 yards per hour 

Light sand... 4 "6 " " 



202 EARTHWORK — EXCAVATIOK. 

By blasting : 

One pound of black powder in small blasts will loosen about 
4^ tons of hard rock, in large blasts about 2^^ tons; one pound 
of dynamite from 6 to 10 tons. 

Removing Earth. — The removal of the loosened material is 
effected by throwing or *' casting" with a shovel when the 
borizoutal distance does not exceed 12 feet and the vertical 6 feet. 

B}^ shovelling into wheelbarrows when the distance is under 
200 feet. 

By shovelling into one-horse carts or two-horse trucks or dump- 
wagons when the distance is great. 

In excavating a large area of light depth in moderately com- 
pact material the loosening is performed with ploughs, and the re- 
moval with scrapers, either drag or wheeled, which automatically 
pick up the loosened material. 

In earth excavations of sufficient magnitude steam-shovels are 
employed for loosening and loading the loosened material into 
dump-cars running on a track and hauled by horses or locomo- 
tives. 

The quantity of material which a man can shovel into a vehicle 
in a given time depends upon the weight of the material. 

The average quantity shovelled into a cart per man per hour 
is : 

Loose earth or sand 2.0 cubic yards 

Olay and heavy soils 1.7 " ** 

Rock. 1.0 cubic yard 

The average speed of horses in hauling is about 200 ft. per 
minute. 

The economical lengtli of haul with drag-scrapers is about 150 
ft., wheeled scrapers 500 ft., wheelbarrows 250 ft., one-horse 
dump-carts 600 ft., two-horse dump-wagons 1000 ft. For hauls 
exceeding a thousand feet a track of light rails with dump-cars 
drawn by horses or light locomotives is the most economical. 

The capacity of the vehicles used for moving excavated material 
is about as follows : 

Wheelbarrows 3 to 4 cubic feet 

1-horse dump carts , 18 " 22 

2 " dump-wagons 27 " 45 

Draff-scrapers 3" 7 

Wlieel-scrapers 10 " 17 

Duinp-cai s on rails 27 ** 81 



EARTHWOHIv. — EXCAVATIONS. 20 M 

Excavations. 

New York Building Code, 1899. 

Sec. 22. Excavations. — All excavations for buildings shall be 
properly guarded and protected so as to prevent the same from 
becoming dangerous to life or limb, and shall be shcath-piled 
where necessary to prevent the adjoining earth from caving in, 
by the person or persons causing the excavations to be made. 
Plans filed in the Department of Buildings shall be accompanied 
by a statement of the character of the soil at the level of the 
footings. 

Whenever an excavation of either earth or rock for building 
or other purposes shall be intended to be, or shall be carried to, 
the depth of more than 10 feet below the curb, the person or 
persons causing such excavation to be made shall at all times, 
from the commencement until the completion thereof, if afforded 
the necessary license to enter upon the adjoining land and not 
otherwise, at his or their own expense, preserve any adjoining or 
contiguous wall or walls, structure or structures from injury, 
and support the same by proper foundations, so that the said 
wall or walls, structure or structures, shall be and remain prac- 
tically as safe as before such excavation was commenced, whether 
the said adjoining or contiguous wall or walls, structure or struc- 
tures, are down more or less than 10 feet below the curb. If 
the necessary license is not accorded to the person or persons 
making such excavation, then it shall be the duty of the owner 
refusing to grant such license to make the adjoining or con 
tiguous wall or walls, structure or structures, safe and sup- 
port the same by proper foundations so that adjoining excava- 
tions may be made, and shall be permitted to enter upon the 
premises where such excavation is being made for that purpose, 
when necessary. If such excavation shall not be intended to be, 
or shall not be carried to, a depth of more than 10 feet below 
the curb, the owner or owners of such adjoining or contiguous 
wall or walls, structure or structures, shall preserve the same 
from injury, and so support the same by proper foundations tiiat 
it or they shall be and remain practically as safe as before such 
excavation was commenced, and shall be permitted to enter upon 
the premises where *such excavation is being made 'for tluit pur- 
pose when necessary. 



2025 EARTHWORFC. — ElCAYATIOKS. 

In case an adjoining party wall is intended to be used by the 
person or persons causing the excavation to be made, and such 
party wall is in good condition and sufficient for the uses of the 
adjoining building, then and in such case the person or persons 
causing the excavatiojis to be made shall, at his or their own 
expense, preserve such party wall from injury and support the 
same by proper foundations, so that said party wall shall be and 
remain practically as safe as before the excavation was com- 
menced. 

If the person or persons whose duty it shall be to preserve or 
protect any wall or walls, structure or structures from injury 
shall neglect or fail so to do after having had a notice of 
24 hours from the Department of Buildings, then the Commis- 
sioner of Buildings may enter upon the premises and employ such 
labor, and furnish such materials, and take such steps as, in his 
judgment, may be necessary to make the same safe and secure, 
or to prevent the same from becoming unsafe or dangerous, at 
the expense of the person or persons whose duty it is to keep the 
same safe and secure. Any party doing the said work, or any 
part thereof, under and by direction of the said Department of 
Buildings, may bring and maintain an action against the person 
or persons last herein referred to, to recover the value of the 
work done and materials furnished in and about the said prem- 
ises in the same manner as if he had been employed to do the 
said work by the said person or persons. When an excavation 
is made on any lot, the person or persons causing such excava- 
tion to be made shall build, at his or their own cost and expense, 
a retaining wall to support the adjoining earth, and such retain- 
ing wall shall be carried to the height of the adjoining earth, 
and be properly protected by coping. The thickness of a retain- 
ing wall at its base shall be in no case less than one fourth of its 
height. 



EARTHWORK — ROCK EXCAVATION. 203 



Kock Excavation. 

Excavation in hard rock is usually performed by means of 
some explosive inserted in a hole bored in the rock, which when 
ignited loosens the mass and permits of its being broken up into 
pieces easily removed. 

Drilling. — Holes for blasting rock are bored either by hand- or 
machine-drills. Shallow cuts, loose boulders, etc., are more 
cheaply bored by hand, but deep and extensive cuttings are more 
economically carried out by the use of machine-drills operated 
either by steam, compressed air, or electricity. 

Hand-drilling is divided into three classes, viz., single' 
handed, in which one man with a set of short drills and a hand- 
hammer bores the holes; douhle-lianded, in which one man 
holds and turns the drill while one or two men strike it alter- 
nately; and churn- or jumper-drilling , in which one or two men 
use a drill called a churn or jumper — the operation consists in 
raising the drill, turning it slightly, and letting it drop. 

The speed with which holes may be bored in rock varies of 
course with the hardness of the rock and the diameter of the 
hole. The smaller the diameter of the hole the greater the depth 
that can be bored in a given time; and the depth will be greater 
in proportion than the decrease of the diameter. 

The average rate of progress made by a good drillman working 
a churn-drill in granite and the harder rocks is about as follows; 

Diam. of Depth bored 

Drill. per Hour. 

Inches. Inches. 

3 4 

2^ 5 

2i 6 

2 8 

If 10 

When the hole exceeds four feet in depth two men are required 
to operate the drill. 

Machine-drilling. — Machine-drills bore holes from f to 6 
inches in diameter. The rate of progress is controlled by the 
same conditions as hand-drilling, and ranges from three to ten 
feet per hour, depending on the character of the rock and the size 
of the machine. 



204 EARTHWORK. — ROCK EXCAVATIOJST. 

Size of Holes. — The diameter tmd depth of the hole will vary 
with the quantity of rock to be loosened, and also with the 
strength of the explosive to be used. 

Blasting. — The quantity of explosive required to loosen a 
given amount of rock depends upon the character of the rock, 
the kind of the explosive, and largely upon a judicious selection 
of the direction of the hole with respect to the *'lay"of the 
strata. 

It is usual to allow f of a pound of black powder to each cubic 
yard of solid rock, or 1 lb. of dynamite to 8 or 10 yards. The 
actual quantity of explosive required will vary with the nature 
of the rock and its degree of compactness or looseness, the latter 
requiring the largest quantity. 

The quantity of explosive required for a given blast may be 
approximately calculated by the following formula: 

If E = the quantity of explosive in pounds, and 

L = the line of least resistance that is, the shortest distance 
from the center of the charge to the surface of the 
rock, then 
E= CL'- 

G — .032 for blasting powder; 
:=.C05 '* '* cotton; 
— .003 *' nitroglycerine and dynamite. 

In blasting no loud report should be heard nor stones be 
thrown out. The best effect is produced when the report is 
trifling, and when the mass is lifted and thoroughly fractured 
without the projection of fragments. If the rock be only shaken 
by a blast and not moved outward, a second charge in the same 
hole will be very effective. 

Explosives. — Most of the explosives used consist of a pow- 
dered substance, partly saturated with nitroglycerine, a fluid pro- 
duced by mixing glycerine with nitric and sulphuric acids. 

Pure nitroglycerine at 60° F. has a specific gravity of 1.6. It 
is odorless, nearly or quite colorless, and has a sweetish burning 
taste. It is poisonous, even in very small quantities. Handling 
it is apt to cause headaches. It is insoluble in water. At about 
o06° P. it takes fire, and if unconfined burns harmlessly, unless it 
is in such quantity that a part of it before coming in contact 
witli air becomes heated to the exploding-point, which is about 
380° F. From its liability to explosion through accidental per- 



EARTHWORK. — ROCK EXCAVATIOIS". 205 

ciiss'ou, leakiige, etc., it is rarely used in the liquid state in ordi 
nary qutirrying or blasting. 

Dynamite is the name applied to any explosive which contains 
nitroglyceriue mixed with a granular absorbent. The nitroglyc- 
erine undergoes no change in composition by being absorbed ; the 
office of the absorbent is to act as a cushion and so protect the 
nitro-glycerine from percussion. 

Dyuamite is classed according to the percentage of nitroglyc- 
erine present. No. 1 contains 75 per cent, and from that down 
to 15 per cent. 

Dynamite is slow to catch fire ; when ignited in the air and un- 
confined it burns fiercely ; if in large quantity or partly confined 
explosion may ensue. 

Dynamite of all grades freezes at about 42° F. When in this 
condition it cannot be completely exploded, and must be thawed 
before use. This must be done gradually by leaving it in a warm 
room far from the fire, or by placing it in a metallic vessel, which 
is then placed in another vessel containing hot water. The v^rater 
should not be hotter than can be borne by the hand. 

Dynamite, giant powder, etc., is sold in cylindrical paper- 
covered cartridges from J to 2 inches in diameter, and 6 to 8 
inches long or longer. They are furnished to order of any required 
size, and are packed in boxes containing 25 or 50 lbs. each. The" 
layers of cartridges are separated by sawdust. 

Powder is fired by fuse, and dynamite either by a fuse with a 
detonating-cap, or by a cap connected to the wires of an electric 
battery ; this method is employed where a number of charges are 
to be fired simultaneously and in blasting under water. 

The cap or exploder used with fuse is a hollow copper cylinder, 
about ^ inch in diameter and an inch or two in length. It con- 
tains from 15 to 20 per cent or more of fulminate of mercury 
mixed with other ingredients into a cement, which fills the closed 
end of the cap. The cap is called *' single-force," '* triple- force," 
etc., according to the quantity of explosive it contains. 

The cap used with magneto-electric blasting apparatus is simi- 
lar to that used with fuse, except that its mouth is closed with 
a cork of sulphur cement, through which pass the two wires 
leading from the electric machine. 

The fuse used for dry work is designated as ** single-tape fuse," 
for work in water "double-tape fuse." 

Fuse burns at the rate of about three feet per minute. 



206 PRECAUTIONS TO BE OBSERVED IN BLASTING. 



Precautious to be observed iu Blasting. 

Although it is not desirable and not so effective to produce a 
gre;it shattering and scattering of the broken rock, little attention 
is paid to this point in ordinary blasting operations. But in blast, 
ing near buildings or in the streets of cities special precautions 
must be taken to avoid projecting the fragments of rock to a great 
distance. This can be done by properly regulating the charge, 
and covering over and around the hole with brush and logs. A 
raft of logs chained together or a matting of ropes weighted with 
logs around the edges will prove effective for this purpose. 

Judgment must be exercised as to the grade and quantity o)' 
explosive to be used in any given case. Where it is not objection- 
able to break the rock into small pieces, or where it is desired to 
do so for convenience of removal, the higher grades of dyna 
mite should be selected. Where it is desired to get the rock oug 
in large masses, as in quarrying, the lower grades are preferable 

For soft or decomposed rocks, sand, and earth the lower gradesf 
of dynamite are more suitable. They explode with less sudden- 
ness, and their tendency is rather to upheave large masses of rock, 
etc., than to splinter small masses of it. 

For very difficult work in hard rock and for submarine blast- 
ing the high grades should be used. A small charge of these 
does the same execution as a larger charge of lower grade and of 
course does not require the drilling of so large a hole. In sub- 
marine work their sharp explosions is not deadened by the water. 

In blasting with dynamite the charge should fill the hole as 
completely as possible. If water is not standing in the hole the 
cartridge should be cut open before insertion. 

The higher grades of dynamite require but little tamping. Use 
a wooden tampiug-bar, nevei' a metallic one for any explosive. 

If a charge of dynamite *' hangs fire " it is dangerous to attempt 
to remove it. Remove the tamping all but a few inches in depth, 
and insert another cartridge and try again. 



EARTHWORK.— DREDGIKG, 201 



Dredging. 

For excavating under water dredging-machines of various types 
are employed, as dipper-dredges, clam-shell dredges, ladder-and- 
bucket dredges, hydraulic dredges, etc. 

The dredged material is usually removed in dumpiug-scows, 
except where the material is of such a character that a sand-pump 
or hydraulic dredge can be used ; in this case the material is trans- 
ported and deposited in place entirely by the force of a stream of 
water. 

The limits of the area to be dredged are marked by ranges, 
which may be objects on shore, piles, or buoys. In tidal waters 
a plainly marked gauge is set up, when possible, at a point visible 
from the proposed cut. The required depth is measured from a 
fixed plane — in tidal waters that of mean low water. 

The necessary channel-marks are placed under the direction of 
the engineer, and the contractor is usually made responsible for 
their care and preservation. 

Duty of Inspector. — The inspector should be continually 
present during the prosecution of dredging operations. His duty 
comprises the determining of the proper position of the dredge, 
and if the width and depth of the cut are in accordance with the 
requirements. When scow measurement is to be used for 
ascertaining the amount of dredged material the capacity of the 
scows is carefully computed and the contractor is required to fill 
them each lime to the same extent. The duty of determining 
whether the scows contain full loads devolves upon the inspector. 
In cases of partial lojids he also decides as to the true amount. 

It is usual to make an extra allowance of from one half to one 
foot for the irregularities left in the bottom by the dredge; that 
is, to insure that the minimum depth shall be attained. 

Material dredged from outside the fixed lines or below the per 
mitted excess of a half or one foot is not paid for. 

The increase of scow measurements over measurements in place 
is for rock If to 2; very soft mud, 13 per cent; soft blue mud, 
15 per cent; hard sand, 20 to 30 per cent. 

Loose muck has been found to measure from 15 to 17 per cent 
less in the dredge-bucket than when in place. In hydraulic 
dredging, particularly where there is much fine, light material, 
place measurements equal or exceed scow measuremcMits. 



?08 E4KTHW0RK.— EMBA^^KMENTS. 

^\ 
Eiiibaiikm eiits. 

Embankments are made in three ways: 1. Id one layer. 2. 
In two or more thick layers. 3. In thin layers. 

I . in One Layer. — This being the cheapest and quickest method 
consistent with stability is that followed in all earthworks in 
which there is no reason to the contrary. 

3. In Thick Layers. — This process is used in embankments of 
great height. It consisis in completing the construction of the 
embankment up to a certain heigh: by the process of dumping 
over the end, leaving that layer for a time to settle, and then mak- 
ing a second layer in the same way. 

3. In Thin iMyers. — This process consists in spreading the 
earth in horizontal layers of from 9 to 18 inches deep, and ram- 
ming or rolling each layer so as to make it compact and firm be- 
fore laying down the next layer. Being a tedious and laborious 
process, it is used in special cases only, of which the principal are, 
the filling behind retaining walls, behind wings and abutments of 
bridges and culverts and over their arches, and the embankments 
of reservoirs for water. 

In embankments of great magnitude and where water is to be 
retained by them all the vegetable matter and mould should be 
removed from the site before depositing the materials of the em- 
bankment. 

In forming embankments on hillsides a common practice is 
to simply dump the material on the side slope; this method is in- 
secure, the material so deposited is liable to slip and slide. The 
best method is to cut the surface of the natural slope into steps, 
the number of which will vary with the length of the slope — three 
feet apart is a good distance. No pains should be spared to give 
the material a secure hold, particularly at the toe of the slope. 

The solidity of embankments which are not to be consolidated 
by rolling may be increased l^y filling from the sides towards the 
centre, keeping the sides high with a dip towards the centre. 

Embankments formed by building a narrow bank as a road- 
way for the vehicles transporting the material, and then widen- 
ing it by dumping the earth on the sides, are deficient in compact- 
ness, and are liable to slips and cracks, and will require a long 
lime for complete consolidation. 

When embankments are to be widened by the addition of new 
material the slopes of the old embankment should be cleaned 
fiom vegetable matter and mould and cut into steps or benches; 
otherwise the new material will not unite perfectly with the old. 



FOUNDATIONS. — DUTY OF INSPECTOK. 209 



II. Foundations.* 
Definitions. 

The term *' foundation " is used to designate all that portion of 
any structure which serves only as a basis on which to erect the 
superstructure. 

The term is sometimes applied to that i^ortion of the solid ma- 
terial of the earth upon which the structure rests, and also to the 
artificial arrangements which may be made to support the base. 

The object to be attained in the construction of any founda- 
tion is to form such a solid base for the superstructure that no 
movement shall take place after its erection. But all structures 
built of coarse masonry, whether of stone or brick, will settle to a 
certain extent, and with but few exceptions all soils will become 
compressed under the weight of almost any building. 

The main object, therefore, is not to prevent settlement entirely, 
but to insure that it shall be uniform, so that after the structure 
is finished it will have no cracks or flaws, however irregularly it 
may be disposed over the area of its site. 

Foundations are divided into two great classes, viz., Natural 
and Artificial. Each of them is subdivided into many kinds ac- 
cording to the material of the earth on which the structure is 
founded, the artificial arrangements required, and foundations 
under water. 

Outy of Inspector. 

As the stability and endurance of a structure depend upon the 
character of its foundation, it is of the utmost importance that 
the inspector concentrate his attention to its preparation, to see 
that the instructions of the engineer or architect and the require- 
ments of the specifications are faithfully carried out, and to report 
without delay to his superior any probable source of failure that 
he may detect. There are two principal sources of failure to be 

* For a complete discussion on the many and various methods of prepar- 
ing foundations the reader is referred to " A Practical Treatise on Founda- 
tions," by W. M. Patton; "A Treatise on Masonry Construction," by I O. 
Baker; "Building Superintendence and Construction," and the "Archi- 
tects' and Builders' Pocket-book," by F. E. Kidder, etc. 



210 FOUJSTDATIONS. — NATURAL FOUNDATIONS. 

guarded against, viz., inequality of settlement, pnd lateral escape 
of the supporting material. 

]N^atural Fotiiidations. 

Foundations constructed in situations where the natural soil is 
sufficiently firm to bear the weight of the intended structure. 

The best natural foundation is a stratum of rock or compact 
gravel. 

The foundation should be started from a uniform level, but if 
circumstances prevent it the ground must be carefully benched, 
i. e., cut into horizontal steps, so that the courses of masonry may 
all be perfectly level. 

It must be borne in mind that all masonry-work will settle 
more or less according to the perfection and thickness of the 
joints, and therefore too much care cannot be exercised in the 
case of steps to bring up the foundation course to a uniform level 
with large blocks of stone or with concrete; otherwise the super- 
structure is liable to settle most over the deepest parts on account 
of the greater number of mortar-joints, and thus cause unsightly 
fractures. 

Rock. — In preparing a rock surface see that all loose and de- 
cayed parts are cut away, that the surface is worked or cut into 
horizontal steps, that all hollows where the rock is solid are care- 
fully filled with concrete. 

Sand being practically incompressible forms an excellent 
foundation so long as it can be kept from shifting, but as it has no 
cohesion and acts like a fluid when exposed to running water, it 
must be treated with caution. Care must be exercised to keep 
surface-water from running into the trenches, and if necessary 
drains should be made at the bottom to carry away any water 
that may find its way in. 

Clay is the most deceptive material to build upon. Its inse- 
curity results from the position of its stratum, as well as its elas- 
ticity, from being mixed with marl, etc., and tendency to absorb 
moisture. In dry weather it is very firm, while in wet weather 
it is elastic and unreliable. 

In building on clay great caution must be used to secure good 
drainage, both before and after the work is begun. 

The foundation must be started below the frost-line, for the 
f,' fleet of frost on clay is very great. 

The trenches must be protected from the entrance of water, 
and must be so arranged that water shall not remaiu in them. 



FOUKDATIOI^S. — NATURAL FOUNDATIONS. 211 

In general the less a clay soil is exposed to tlie air and weather, 
and the sooner it is protected from exposure, the better for the 
work. 

Bearing Power of Soils. — New York Building Laws, 1892- 
96: ** Good solid natural earth shall be deemed to safely sustain 
a load of 4 tons to the superficial foot, and the width of footing- 
courses shall be at least sufficient to meet this requirement." 

Chicago Building Ordinances, 1893: 

Pure clay, 15 ft. thick, without admixture of any for- 
eign substance, excepting gravel 3500 lbs. 

Dry sand, 15 ft. or more in thickness, and without ad- 
mixture of clay, loam, or other foreign substance.. 4000 ** 

Clay and sand mixed 3000 ** 

Loads on Foundations. — Chicago Building Ordinances, 1893: 

Per Sq. Ft. 

Concrete foundations 8,000 lbs. 

Foundation-piers of dimension stone 10,000 " 

Brick piers in cement 18,000 to 25,000 " 

Iron rails in concrete 12,000 " 

Steel '' " •* 16,000 " 

Piles c 2.") tons 

Bearing Power of Soils.— Tho maximum load that can be 
placed upon foundations is fixed by law in many cities. 

The maximum load permitted by the New York Building Code, 
1899, is as follows : 

Soft clay 1 ton per sq. ft. 

Clay and sand in layers, wet and springy 2 " '* *' *' 

Loam, clay, or fine sand, firm and dry 3 " " *' '' 

Coarse sand, stiff gravel, or hard clay 4 *' '* ^' '* 

LiOads on Foiiiidations. 

New York Building Code, 1899. 

Sec. 25. When foundations are carried down through earth by 
piers of stone, brick, or concrete in caissons, the loads on same 
shall be not more than 15 tons to the scpiare foot when carried 
down to rock; 10 tons to the square foot when carried down to 
firm gravel or hard clay ; 8 tonstotlu^ s(iuare foot in open cais- 
sons or sheet pik^ tnuiches when cari'ied down to rock. 



2lla FOU]srDATio]srs. — artificial foundations. 

Foundations. 

JVew Fork Building Code, 1899. 

Every building except buildings erected upon solid rock or 
buildings erected upon wharves and piers on the water front, 
shall have foundations of brick, stone, iron, steel, or concrete laid 
not less than 4 feet below the surface of the earth, on the 
solid ground or level surface of rock, or upon piles or ranging 
timbers when solid earth or rock is not found. 

New York Building Code, 1899. 
Sec. 26. Foundation Walls. — Foundation walls shall be 
constructed to include all walls and piers built below the curb 
level, or nearest tier of beams to the curb, to serve as supports 
for walls, piers, columns, girders, posts, or beams. Foundation 
walls shall be built of stone, brick, Portland cement concrete, 
iron, or steel. If built of rubble stone or Portland cement con- 
crete, they shall be at least 8 inches thicker than the wall next 
above them to a depth of 12 feet below the curb level ; and for 
every additional 10 feet, or part thereof, deeper, they shall be 
increased 4 inches in thickness. If built of brick, they shall 
be at least 4 inches thicker than the wall next above them to a 
depth of 12 feet below the curb level; and for every additional 
10 feet, or part thereof, deeper, they shail be increased 4 inches 
in thickness. 

Artificial Foundations. 

The construction of foundations in compressible soils, quick- 
sand, and under water oftentimes requires all the resources of the 
engineer, and causes no little trouble, anxiety, and expense. The 
methods employed are many and varying, comprising coffer- 
dams, cribs, caissons, hollow cylinders, timber and iron piles, 
pneumatic piles, freezing, and other processes. 

Cafssons are of two forms, the "erect" or "open" and the 

" inverted." The former is a strong water-tight box, having 

vertical sides and a bottom of heavy timber, in which the ma- 

•soury is built, and which sinks as the masonry is added, until the 

bottom rests upon the foundation prepared for it. 

The inverted caisson is also a strong water-tight box, open at 
the bottom and closed at the top, upon which tlie structure is 
built, and which sinks as the masonry is added. This style of 
caisson is usually aided in sinking by the pneumatic process, in 
which case it is called a pneumatic caisson. 

The name caisson is also applied to cylinders of cast iron or 



212 FOUKDATIOI^S.— ARTIFICIAL FOUKBATlOKS. 

steel, which are sunk by removing the material from the inside 
either by manual labor or by dredging. 

The processes employed to aid the sinking of inverted caissons 
are called the "vacuum " and the " plenum." 

The vacuum process consists in exhausting the air from the in- 
terior of the caisson, and using the pressure of the atmosphere 
upon top of it to force it down. Exhausting the air allows the 
water to flow past the lower edge into the interior, thus loosening 
the soil. 

The plenum or compressed-air process consists in pumping air 
into the chamber of the caisson, which by its pressure excludes 
the water. An air-lock or entrance provided with suitable doors 
is arranged in the top of the caisson, by which workmen can 
enter to loosen up the soil and otherwise aid in the sinking of the 
caisson vertically by removing and loosening the material at the 
sides. If the loosened material is of a suitable character it is 
removed with a sand-pump; if not, suitable hoisting apparatus is 
provided and it is loaded into buckets by the workmen and 
hoisted out through the air-lock. 

Coffer-dams are temporary enclosures from which water may 
be pumped out so as to allow of work being done within them. 
Their construction varies greatly, depending upon the conditions 
to be met. 

The most perfect form consists of two parallel rows of main 
and sheet piles enclosing between them a vertical wall of clay 
puddle. Simple banks of clay and gravel, or of bags filled with 
clay, or a single row of sheet-piling protected with a bank of 
clay are used where the conditions permit. 

Cribs.— Timber cribs consist of a series of layers of round or 
squared timber, laid alternately lengthwise and crosswise, notched 
and pinned to each other at their intersections, each notch being 
about one fourth the depth of the stick. The crib forms a series 
of square or rectangular cells, which are usually filled with stones. 

Freezing Process. — This process is employed in sinking 
foundation-pits through quicksand and soils saturated with 
water. The Poetsch-Sooysmith process is to sink a series of 
pipes 10 inches in diameter through the earth to the rock: these 
are sunk in a circle around the proposed shaft. Inside of the 10- 
inch pipes 8-inch pipes closed at the bottom are placed, and 
inside of these are placed smaller pipes open at the bottom. 
Each set of the small pipes is connected in a series. A freezing 
mixture is then allowed to flow downw^ards througli one set of 



FOUNDATIONS. — ARTIFICIAL FOUNDATIONS. 218 

the smaller pipes and return upwards through the other. The 
freezing mixture flows from a tank placed at a sufficient height 
to cause the liquid to flow with the desired velocity through the 
pipes. The effect of this process is to freeze the earth into a 
solid wall. 

Grillage is a frame of one or more courses of timber, drift- 
bolted or -pinned to the tops of piles and to each other, upon 
which a floor of thick planks is placed to receive the bottom 
courses of masonry. 

The timbers which rest upon the piles are called caps; they are 
usually about 1 foot square, and are fastened by boring a hole 
through each one into the head of the pile and driving into the 
hole a plain rod or bar of iron having about 25 per cent larger 
cross-section than the hole. 

These rods are called drift-bolts, and are usually either a rod 
1 inch in diameter (driven into a f-inch auger-hole) or a bar 1 
inch square (driven into a |-inch hole). Formerly jag-bolts or 
rag-bolts, i. e., bolts whose sides were jagged or barbed, were 
used for this and similar purposes, but universal experience 
shows that smooth rods hold much better. Round bolts are 
preferable to square, because they do not cut or tear the wood. 
The ends of the rods should be slightly pointed with a hammer. 

Transverse timbers are put on top of the caps and drift-bolted 
to them. As many courses may be added as is necessary, each 
perpendicular to the one below it. The timbers of the top 
course are laid close together, or, as before stated, a floor of 
thick plank is added on top to receive the masonry. 

Grillages formed of iron and steel rails and beams bedded in 
concrete are being extensively employed for the foundations of 
steel and iron buildings. The method employed is to cover the 
bottom of the foundation-pit with a layer of concrete ; on this is 
placed a layer of steel I beams or rails spaced 6 to 8 inches apart 
and the spaces between them filled in with concrete. These are 
covered with a similar set at right angles and concreted, and then 
again with a third or fourth course, and the whole finished flush 
with concrete. 

Before the beams are laid on the concrete it is recommended 
that its surface be covered with two thicknesses of tarred felt 
laid in hot asphalt, and on top of this a layer of cement mortar 
IJ inches thick, in which the beams are bedded. 

Before the beams are laid they should be thoroughly cleansed 
with wire brushes, and while dry either painted with asphalt or 



214 FOUIS^DATIONS.— ARTIFICIAL FOUNDATIOlSrS. 

heated and dipped in asphalt. Before covering the beams with 
the concrete every portion of the metal should be examined, and 
wherever the coating has been scraped off in handling should be 
thoroughly dried and recoated or painted. 

New York Building Code, 1899. 

Sec. 25. Protection of Metal in Foundations.— Where 
metal is incorporated in or forms part of a foundation it shall be 
thoroughly protected from rust by paint, asphaltum, concrete, 
or by such materials and in such manner as may be approved by 
the Commissioner of Buildings. When footings of iron or steel 
for columns are placed below the water level, they shall be simi- 
larly coated or enclosed in concrete for preservation against rust. 

Piles. 

The materials employed for piles are timber, rolled, forged, 
or cast steel, and wrought -iron pipes and cast-iron cylinders. 

Timber Piles are generally round, and have a length of 
about twenty times their mean diameter. The diameter of the 
butt varies from 9 to 18 inches. 

The timber emploj^ed for piles varies with the conditions. 
For soft or luediam soils or situations in which the piles will be 
always under water spruce and hemlock are frequently used. For 
firmer soils the hard pines, fir, elm, and beech are generally used. 
For still more compact soils, and where the pile is alternately 
wet and dry, white or black oak and yellow or Southern pine are 
used. 

Where piles are exposed to tide-water they are generally 
driven with the bark on. In other cases it is not essential. 

In Southern waters special precautions are necessary to pro- 
tect the piles from the ravages of the Teredo. In Florida the 
palmetto-wood is extensively used on account of its being little 
attacked by the Teredo, 

III driving through hard ground the point of the pile is some- 
times protected with a shoe of either cast or wrought iron, and 
the head bound with an iron hoop to prevent splitting. 

As a rule, piles drive better when cut off square than when 
pointed; iron shoes generally si rip off before the pile has pene- 
trated far. 



FOUKDATIOJSrS. — DESCRIPTIOK OF PILES. 215 



Description of Piles. 

Anchor-pile : A pile driven at some distance from another, 
usually at ay angle, to which the face-pile is fastened by an iron 
tie-rod to prevent the face-pile springing or being forced out of 
its position. 

Bearing-piles are long piles driven into the soil to act as 
pillars in supporting the load. They may either be driven 
through the soft stratum until they reach a firm stratum and 
penetrate a short distance into it, or, if that be impracticable, 
they may be supported wholly by the friction of the soft 
stratum. 

The load which bearing-piles will carry depends upon the 
character of the material into which they are driven. 

In sand and soft clays piles driven to depths of 40 to 50 ft. 
will carry safely from 20 to 30 tons per pile. If driven through 
to rock or hardpan^ so that the pile becomes a timber column, 
they will carry safely 50 to 70 tons per pile. Piles driven into 
soft, silty, and marshy soils, and penetrating to 60, 80, or even 100 
or more feet without reaching firm soil of any kind, may carry 
safely loads from 10 to 25 tons. 

Close Pile : A pile of square timber driven close to another. 

Disk-pile : A bearing-pile near the foot of which a disk is 
keyed or bolted to give additional bearing power. 

False-pile : An additional length added to a pile after driv- 
ing. 

Fender Pile : A pile driven to ward off blows from floating 
bodies. 

Filling-piles : Piles filling the space between gauge-piles. 

Foundation-pile : One driven to increase the supporting- 
power of the soil under a foundation. 

Gauge-piles : Piles placed to mark the desired course of a 
row of piles. 

In dredging, piles driven to mark the course and depth of the 
excavations. 

Guide-piles : Piles which limit the field of operations in 
dredging. 

Hollow Piles. — Cylinders of cast iron sunk by excavating 
from the interior. They are cast in various lengths and diame- 
ters. Short lengths are usually employed for those of small di- 
ameter, sections being added as they sink, the sections being fas- 



216 FOUKDATIOKS. — DESCRIPTIOK OF PILES. 

tened together bv internal flanges. When they have reached the 
stratum upon which they are to rest they are usually filled with 
concrete. If used to resist sea-water the iron should be close- 
grained white iron. 

Iron and Steel Piles. — Both cast and wrought iron and 
steel are employed for ordinary bearing-piles, sheet-piles, and for 
cylinders. Iron cylinders are usually sunk either b}^ dredging 
the soil from the inside or by the pneumatic process. 

Cast-iron piles are used as substitutes for w^ooden ones. Lugs 
or flanges are usually cast on the sides of the piles, to which 
bracing may be attached for securing them in position. A wood 
block is laid upon top of the pile to receive the blows of the ham- 
mer used in driving it, and after being driven a cap with a socket 
in its lower side is placed upon the pile to receive the load. 

Solid rolled-steel piles are driven in the same manner as timber 
piles, either with a hammer, machine, or water-jet. 

Pneumatic-pile : A metal cylinder similar to a hollow pile, 
but sunk by atmospheric pressure. 

Sand-piles : The practical incompressibility of sand renders 
it an excellent foundation wherever it can be protected from wash 
by water. The form in which it is most successfully used is that 
of piles. The ground is prepared by driving timber piles, then 
withdrawing them and filling the holes with sand. 

The sand used should be moderately fine, angular-grained, 
clean, and uniform in size. If wet it should be rammed with 
considerable force. If dry it arranges itself better, and when in 
place may be moistened and rammed. 

Screw-piles are piles which are screwed into the stratum in 
which they are to stand. They are ordinary piles of timber or 
iron (the latter usually hollow), to the bottom of which a screw- 
disk, consisting of a single turn of the spiral, similar to the 
bottom turn of an auger, is fastened by bolts or pins; and instead 
of driving them into the ground they are forced in by turning 
them with levers or machinery suitable for the purpose. The 
screw-disks vary in diameter from 1 to 6 feet. The water-jet is 
sometimes employe I by applying it to the under, upper, or both 
sides of the disk for the purpose of reducing the resistance. 

Sheet- PILES are flat piles, usually of plank, either tongued and 
grooved or grooved only, in'n which a strip or tongue is driven; 
or they may be of squared timber, in w^hich case they are called 
"close piles," or of sheet iron. The timber ones are of any 
breadth that can be procured, and from 2 to 10 inches thick, and 



FOUNDATIONS. — DESCRIFTIOJST OF PILES. 217 

are sharpened at the lower end to an edge wholly from one side; 
this point being placed next to the last pile driven tends to crowd 
them together and make tighter joints (the angle formed at the 
point should be 30°). In stony ground they are shod with iron. 

When a space is to be enclosed with sheet-piling two rows of 
guide-piles are first driven at regular intervals of from 6 to 10 
feet, and to opposite sides of these near the top are notched or 
bolted a pair of parallel string-pieces or "wales," from 5 to 10 
inches square, so fastened to the guide-piles as to leave a space 
between the wales equal to the thickness of the sheet-piles. If 
the sheeting is to stand more than 8 or 10 feet above the ground 
a second pair of wales is required near the level of the ground. 
The sheet-piles are driven between the wales, working from each 
end towards the middle of the space between a pair of guide- piles, 
so that the last or central pile acts as a wedge to tighten the 
whole. 

Sheet-piles are driven either by mauls wielded by men or by a pile- 
driving machine. Ordinary planks are also used for sheet-piling, 
being driven with a lap; such piling is designated as '* single-lap," 
"double-lap," and '' triple-lap." The latter is also known as the 
" Wakefield triple-lap sheet-piling." 

Short Piles are driven in order to compress and consolidate 
the soil. They are usually of round timbers, from 6 to 9 inches 
in diameter and from 6 to 12 feet long, and are driven as close 
to each other as is practicable without causing the neighboring 
piles to rise. The centre pile should be driven first, then the next 
without, and so on to the outside row. 

Test-pile : A pile driven to test the character of the soil. 



218 rOU-t^DATIONS. — PILE-DKIVIi^G. 



Pile-driving. 

Timber piles are driven either point or butt end down; the latter 
is considered the better method. 

When piles are directed to be sharpened the points should have 
a length of from one and a half times to twice the diameter. 

To prevent the head of the pile from being broomed or split by 
the blows of the driving-ram it is bound with a wrought-iron 
hoop, 2 to 3 inches wide and J- to 1 inch thick. Instead of the 
wrought-iron band a cast-iron cap is sometimes used. It consists 
of a block with a tapering recess above and below, the cham- 
fered head of the pile fitting into the one below, and a cushion- 
piece of hard wood upon which the hammer falls fitting into the 
one above 

When brooming occurs the broomed part should be cut off, 
because a broomed head cushions the blow and dissipates it with- 
out any useful effect. 

Piles that split or broom excessively or are otherwise injured 
during the driving must be drawn out. 

Bouncing of the hammer occurs when the pile refuses to drive 
further, or it may be caused by the hammer being too light, or its 
striking velocity being too great, or both. The remedy for 
bouncing is to diminish the fall. A slight bounce should occur 
at the end of every blow. 

Excessive hammering on piles which refuse to move should be 
avoided, as they are liable to be crippled, split, or broken below 
the ground, which will pass unnoticed and may be the cause of 
future failure. 

As a general rule, a heavy hammer with a low fall drives more 
pleasantly than a light one with a high fall. More blows can be 
made in the same time with a low fall, and this gives less time 
for the soil to compact itself around the piles between the blows. 
At times a pile may resist the hammer after sinking some distance, 
but start again after a short rest; or it may refuse a heavy ham 
mer and start under a light one. It may drive slowly at first, and 
more rapidly afterwards, from causes that may be difficult to 
discover. The driving of one sometimes causes adjacent ones 
previously driven, to spring upwards several feet. The driving 
of piles in soft ground oi mud will generally cause an adjacent 
one previously driven to lean outwards unless means be taken to 
prevent it. 

A pile may rest upon rock and yet be very weak,, for if driven 



^ 



FOUNDATIONS. — PILE-DRIVING 219 

through very soft soil all the pressure is borne by the sharp 
point, and the pile becomes merely a column in a worse condition 
than a pillar with one rounded end. In such soils the piles need 
very little sharpening ; indeed, had better be driven without 
any, and better butt end down. 

Solid metal piles are usually of uniform diameter and are 
driven with either blunt or sharpened points. 

Piles are driven by machines called pile-drivers. They consist 
essentially of two upright guides or leads, often of great height, 
erected upon a platform, or on a barge when used in water 
These guides serve to hold the pile vertical while being driven, 
and also hold and guide the hammer used in driving. This is a 
block of iron called a ram, monkey, or hammer, weighing any 
where from 800 to 4000 pounds; average weight, from 2000 to 
3000 pounds. The accessories are a hoisting-engine for raising 
the hammer and the devices for allowing it to drop freely on the 
heads of the piles. 

The steam-hammer is also employed for driving piles, and has 
certain advantages over the ordinary form, the chief of which 
lies in the great rapidity with which the blows follow one 
another, allowing no time for the disturbed earth, sand, etc., to 
recompact itself around the sides and under the foot of the pile. 
It is less liable than others to split and broom the piles, so that 
these may be of softer and cheaper wood. The piles are not so 
liable to " dodge 'or *' get out of line."' 

When piles have to be driven below the end of the leaders of 
the pile-driver 2^ follower is used. This is made from a pile of 
suitable length placed on top of the pile to be driven; to prevent 
its bouncing off caps of cast iron are used, one end being bolted 
to the follower and the other end fitting over the head of the 
pile. 

Piles are also driven by the *• water- jet." This process consists 
of an iron pipe fastened by staples to the side of the pile, its 
lower end placed near the point of the pile and its upper end 
connected by a hose to a force-pump. The pile can be sunk 
through almost any material, except hardpan and rock, by forc- 
ing water through the pipe. It seems to make very little differ- 
ence, either in the rapidity of sinking or in the accuracj^ with 
which the pile preserves its position, whether the nozzle is ex- 
actly under the middle of the pile or not 

The efficiency of the jet depends upon the increased lluidity 
given the material into which the pilf's iire sunk, the uctua] dis 



220 



FOUXDATIOis^S. — PILIX-DKIVING, 



placement of material being small Hence the efficiency of the 
jet is greatest in clear sand, mud. or soft clay, in gravel or in 
sand containing a large percentage of gravel, or in hard clay the 
jet is almost useless. For inese reasons the engine pump hose 
and nozzle should be arranged to deliver large quantities of 
water with a moderate force rather than smaller quantities with 
high initial velocity. In gravel or in sand containing gravel 
some benefit might result from a velocity sufficient to displace 
the pebbles and drive them from the vicinity of the pile. 

The error most frequently made in the application of the 
water- jet is in using pumps with insufficient capacity 

The approximate volume of water required per minute per 
iuch of average diameter of pile for penetrations under 40 feet 
is 16 gallons, for greater depths the increase in the volume of 
water is approximately at the rate of 4 gallons per inch of diam- 
eter of pile per minute foi each additional 10 feet of penetration. 

The number and size oi pipes required for various depths are 
about as follows ; 



Deptti 
of Penetration 


Diameter 
of Pipe 


Number 
of Pipes. 


Diametei 
of Nozzle 


Feet. 


Inches. 


Inches. 


20 


2 


1 


1 


30 


2^ 


1 


u 


40 


2i 


2 


n 


60 


2i 


2 


1 


60 


2i 


2 


i 



When the descent of the pile becomes slow, or it sticks or 
'•brings up '' in some tenacious material, it can usually be started 
by striking a few blows with the pile-driving hammer, or by 
raising the pile about 6 inches and allowing it to drop suddenly, 
with the jet in operation. By repeating the operation as rapidly 
as possible the obstruction will generally be overcome. 

It is an advantage to use an ordinary pile-driving machine for 
sinking piles with the water-jet The hammer being allowed to 
rest upon the head of the pile aids in accelerating the descent, 
and light blows can be struck as often as may appear necessary. 
The efficiency of the jet can also be greatly increased by bringing 
the weight of the pontoon upon which the machinery is placed 
to bear upon the pile by means of a block and tackle. 



FOUNDATIONS. — INSPECTION OF PILES. 221 

Splicing Piles —It frequently happens in driving piles in 
swampy places, for false works, etc., that a single pile is not long 
enough, in which case two are spliced together A common 
rr«thod of doing this is as follows. After the first pile is driven 
its head is cut off square, a hole 2 inches in diameter and 12 inches 
deep is bored in its head, and an oak treenail or dowel-pin 23 
inches long is driven into the hole; another pile similarly squared 
and bored is placed upon the lower pile, and the driving con- 
tinued. Spliced in this way the pile is deficient in lateral stiff- 
ness, and the upper section is liable to bounce off while driving. 
It is better to reinforce the splice by flattening the sides of the 
piles and nailing on with, say, 8 inch spike four or more pieces 
2 or 3 inches thick, 4 or 5 inches wide, and 4 to 6 feet long. 

Inspection of Piles. 

As soon as the piles are delivered on the work they must 
be carefully examined, both as regards dimensions and qual- 
ity, and those failing to meet the specification requirements 
must be conspicuously marked with paint or burning-iron 
to indicate that they are condemned. All condemned piles 
must be removed as speedily as possible; otherwise many of 
them are liable to find their way into the work. 

Round piles should be made from live timber, free from 
cracks, wind-shakes, and large knots. They should be so straight 
that a straight line taken in any direction from the centre of 
each end of the pile and run the length of it shall show 
that the pile is at no point over one eighth of its diameter at such 
point out of a straight line. 

It is very necessary that the inspector watch the driving of 
ever}^ pile, for there is some danger that piles shorter than re- 
quired may be introduced into the work, or that workmen, to 
save themselves trouble or for other reasons, may drive a pile 
only a portion of the required distance, and then*cut it off. 

In cutting off the heads of piles they must be sawn level. 
Usually, however, they are sawn so that the heads are either 
concave or inclined. Both cases are due to the manner of hold- 
ing the saw. Such defects are not permissible, and pile-heads 
so cut must be recut in the proper manner. 

Piles frequently get considerably out of line in driving. In 
some cases they may be forced back with a block and tackle 
or a jack-screw, 



222 FOUXDATIOXS.— CLA.Y PUDDLE. 

The inspector is usually required to keep a record of the pile- 
driving. The following form will be found convenient: 

PILE-DRIVING RECORD. 



f 





Pile Number. 




1 




3 


4 


5 


6 


7 


Date 




Kind of timber 




Lensrth • 




D ameter butt 




point. . 

Tjeiiorth driven 




*' cut off 




"VVeio-ht of hammer 




Fall 




Xo of blows 




Penetration, 10 blow^s. 

*< 20 " 




*' 30 " 




40 " . 

** last blow 




Driven with follower . 




Weis^ht of " 




Driven noint down 




" butt " 





Piles. 

New York Building Code, 1S90. 
Sec. 25. — Piles intended to sustain a wall, pier, or post shall 
be spaced not more than 36 or less than 20 inches on centre, 
and they shall be driven to a solid bearing if practicable to do so, 
and the number of such pibs shall be sufficient to support the 
superstructure proposed. No pile shall be used of less dimen- 
sions than 5 inches at the small end and 10 inches at the butt for 
short piles or piles 20 feet or less in length, and 12 inches at the 
butt for long piles or piles more than 20 feet in length. No pile 
shall be weighted with a load exceeding 40,000 pounds. When 
a pile is not driven to refusal, its safe sustaining power shall 
be determined by the following formula : Twice the weight of 
the hammer in tons multiplied by the height of the fall in feet 
divided by least penetration of pile under the last blow in inches 
plus one. The Commission^T of Buildings shall be notified of 
the time when such test piles will be driven, that he may be 



FOUKDATIOKS. — CLAY PUDDLE. 223 

present ia person or by representative. The tops of all piles 
shall be cut off below the lowest water line. When requii-ed, 
concrete shall be rammed down in the interspaces between tli^ 
heads of the piles to a depth and thickness of not less than 12 
inches and for 1 foot in width outside of the piles. Where 
ranging and capping timbers are laid on piles for foundations, 
they shall be of hard wood not less than 6 inches thick and 
properly joined together, and their tops laid below the lowest 
water line. Wood piles may be used for the foundations under 
frame buildings built over the water or on salt meadow land, 
in which case the piles may project above the water a sufficient 
height to raise the building above high tide, and the building 
may be placed directly thereon without other foundation. 

Clay Puddle. 

Clay puddle is a mass of cla}^ and sand worked into a plastic con- 
dition with water. It is used for filling coffer-dams, for making 
embankments and reservoirs water-tight, and for protecting 
masonry against the penetration of water from behind. 

Quality of Clay. — The clays best suited for puddle are 
opaque, and not crystallized, should exhibit a dull earthy fracture, 
exhale when breathed upon a peculiar faint odor termed ''argil- 
laceous," should be unctuous to the touch, free from gritty matter, 
and form a plastic paste with water. 

The important properties of clay for making good puddle are its 
tenacity or cohesion and its power of retaining water. The tenac- 
ity of a clay may be tested by working up a small quantity with 
water into a thoroughly plastic condition, and forming it by hand 
into a roll about 1 to 1^ inches in diameter b}'' 10 or 12 inches in 
length. If such a roll is sufficiently cohesive not to break on be- 
ing suspended by one end while wet the tenacity of the material 
is ample. 

To test its power of retaining water one to two cubic yards 
should be worked with water to a compact homogeneous plastic 
condition, and then a hollow should be formed in the centre of the 
mass capable of holding four or five gallons of water. After fill- 
ing the hollow with water it should be covered over to prevent 
evaporation and left for about 24 hours, when its capability of 
holding water will be indicated by the presence or absence of 
water in the hollow. 

The clay should be freed from large stones and vegetable matter, 
and just sufficient sand and water added to make a homogeneous 
mass. If there is too little sand the puddle will crack by shrink- 
age in drying, and if too much it will be permeable. 



224 FOUNDATIONS. — CONCRETE. 

Puddling. — The operation of puddliug consists in chopping 
the cLiy in layers of about 3 inches thick wilh spades aided by the 
addition of sufficient water to reduce it to a pasty condition. After 
each chop and before withdrawing the spade it should be given 
a hinging motion so as to permit the water to pass through. 

The spade should pass through the upper layer into the lower 
layer so as to cause the layers to bond together. 

The test for thorough puddling is that the spade will pass 
through the layer with ease, which it will not do if there are any 
dry hard lumps. 

Sometimes in place of spades harrows are used, each layer of 
clay bein^: thoroughly harrowed aided by water and then rolled 
with a grooved roller to compact it. 

The finished puddle should not be exposed to the drying action 
of the air, but should be covered with a layer of dry clay or sand. 

Concrete. 

Concrete is a species of artificial stone composed of (1) the 
matrix, which may be either lime or cement mortar, usually the 
latter, and (2) the aggregate, which may be any hard material, as 
gravel, shingle, broken stone, shells, brick, slag, etc. 

The essential quality of concrete seems to be that the material 
of the aggregate should be of small dimensions, so that the 
cementing medium may act in every direction round them, and 
that the latter should on no account be more in quantity than is 
necessary for that purpose. The aggregate Should be of different 
sizes, so that the smaller shall tit into the voids between the 
larger. This requires less mortar and with good aggregate gives 
a stronger concrete. Broken stone is the most common aggregate. 

To insure compact packing the aggregate should consist of a 
mixture of broken stone ranging from 1 to 3 inches, and pebbles 
which are at least equal to the strength of the mortar. Sun-dried 
or rain-soaked material must be strictly avoided. Gravel and 
shingle should be screened to remove the larger-sized pebbles, 
dirt, and vegetable matter, and should be washed if they contain 
silt or loam. The broken stone if mixed with dust or dirt 
must be washed before use. 

Strength of Concrete. — The resistance of concrete to crush- 
ing ranges from about 600 to 1400 pounds per sq. in. It depends 
upon the kind and amount of cement and upon the kind, size, and 
strength of the aggregate. The transverse strength ranges be- 
tween 50 and 400 pounds. 

Weigut of Concrete. — A cubic yard weighs from 2500 to 
3000 pounds according to its composition. 



PROPORTIOKS OF MATERIALS FOR COKCRETE. 225 



Proportions of Materials for Concrete. 

To manufacture one cubic yard of concrete the following 
quantities of materials are required : 

BROKEN-STONfi-AND- GRAVEL CONCRETE. 

Broken-stone 60% of its bulk voids 1 cubic yard 

Gravel to fill voids in the stone J * * " 

Sand to fill voids in the gravel J ** '* 

Cement to fill voids in the sand i ** ** 

Broken- STONE Concrete. 

Broken stone 50% of its bulk voids 1 cubic yard 

Sand to fill voids in the stone | *' " 

Cement to fill voids in the sand ^ " '* 

Gravel Concrete. 

Gravel i of its bulk voids 1 cubic yard 

Sand to fill voids in the gravel i ' ' ' * 

Cement to fill voids in the sand J ** '* 

Concrete composed of 1 part Rosendale cement, 2 parts of sand, 
and 5 parts of broken stone requires^ 

Broken stone. . «. 0.92 cubic yard 

Sand 0.37 *' 

Cement 1.43 barrels 

The usual proportions of the materials in concrete are : 

Rosendale Cement Concrete. 

Rosendale cement 1 part 

Sand 2 parts 

Broken stone 3 to 4 " 

Portland Cement Concrete. 

Portland cement 1 part 

Sand 2 to 3 parts 

Broken stone or gravel » . . . . 3 to 7 " 

To make 100 cubic feet of concrete of the proportions 1 to 6 
will require 5 bbls. cement (oiiginal package) nnd 4.4 yards of 
stoni" and sand. 



226 MIXING CONCKETE. 

One biirrel of Portland cement, 2 bbls. sand, and 5 bbls. of 
broken stone will make about 20 cubic feet of concrete; these eight 
volumes will on setting fill a space of about 5.2 volumes^ 

Mixing Concrete. — The concrete may be mixed by hand or 
machinery. In hand-mixing the cement and sand are mixed 
dry. About half the sand to be used in a batch of concrete is 
spread evenly over the mortar-board, then the dry cement is 
spread evenly over the sand, and then the remainder of the sand 
is spread on lop of the cement. The sand and cement are then 
mixed with a hoe or by turning and re- turning with a shovel. It 
is very important that the sand and cement be thoroughly mixed. 
A basin is then formed by drawing the mixed sand and cement 
to the outer edges of the board, and the whole amount of water 
required is poured into it. The sand and cement are then thrown 
back upon the water and thoroughly mixed with the hoe or 
shovel into a stiff mortar and then levelled off. The broken stone 
or gravel should be sprinkled with sufficient water to remove all 
dust and thoroughly wet the entire surface. The amount of 
water required for this purpose will vary considerably with the 
absorbent power of the stone and the temperature of the .air. 
The wet stone is then spread evenly over the top of the mortar 
and the whole mass thoroughly mixed by turning over with the 
shovel. Two, three, or more turnings may be necessary. It 
should be turned until every stone is coated with mortar, and 
the entire mass presents the uniform color of the cement, and the 
mortar and stones are uniformly distributed. When the aggregate 
consists of broken brick or other porous material it should be 
thoroughly wetted and time allowed for absorption previous to 
use; otherwise it will take away part of the water necessary to 
effect the setting of the cement. 

When the concrete is ready for use it should be quite coher- 
ent and capable of standing at a steep slope without the w^ater 
running from it. 

The rules and the practice governing the mixing of concrete 
vary as widely as the proportion of the ingredients. It may be 
stated in general that if too much time is not consumed in mixing 
the wet materials a good result can be obtained by any of the 
many ways practised, if only the mixing is thorough. With four 
men the time required for mixing one cubic yard is about ten 
minutes. 

Wluitevcr the method adopted for mixing the concrete, it is 
advisable for the inspector to be constantly present during the 



LAYING CONCRETE. 227 

operation, as the temptatioa to economize on the cement and to 
add an excess of water to lighten the labor of mixing is very 
great. ^ 

Laying Concrete. — Concrete is usually deposited in layers, 
the thickness of which is generally stated in the specifications for 
the particular work (the thickness varies between 6 and 12 in.) 
The concrete must be carefully deposited in place. A very 
common practice is to tip it from a height of several feet into the 
trench. This process is objected to by the best authorities on 
the ground that the heavy and light portions separate while fall- 
ing, and that the concrete is, therefore, not uniform throughout 
its mass. 

The best method is to wheel the concrete in barrows, imme 
diately after mixing, to the place where it is to be laid, gently 
tipping or sliding it into position and at once ramming it 

The ramming should be done before the cement begins to set, 
and should be continued until the water begins to ooze out upon 
the upper surface. When this occurs it indicates a sufficient 
degree of compactness. A gelatinous or quicksand condition of 
the mass indicates that too much water was used in mixing. Too 
severe or long continued pounding injures the strength by forcing 
the stones to the bottom of the layers and by disturbing the 
incipient ''set" of the cement The ramming in one spot or 
locality should occupy not less than three minutes and not more 
than five. 

The rammers need not be very heavy 10 to 15 lbs. will be suf- 
ficient. Square ones should measure from 6 to 8 in on a side 
and round ones from 8 to 12 in, in diameter 

After each layer has been rammed it should be allowed suffi 
cient time to " set," without walking on it or in other ways dis- 
turbing it. If successive layers are to be laid the surface of the 
one already set should be swept clean, wetted, and made rough 
by means of a pick for the reception of the next layer. 

Great care should be observed in joining the work of one day 
to that of the next. The last layer should be thoroughly com- 
pacted and left with a slight excess of mortar, It should be tin 
ished with a level surface, and when partially set should be 
scratched with a pointed stick and covered with planks canvas^ 
or straw. In the morning, immediately before the application 
of the next la3^er. the surface should be swept clean, nioistcuod 
with water, and painted with a wash of neat cement mixed with 
water to the consistency of cream This should be put on in 



228 DEPOSITING COXCRETE UNDER WATER. 

excess and brushed thoroughly back and forth upon the surface 
so as to insure a close contact therewith. 

Depositing Concrete under Water — In laying concrete 
under water an essential requisite is that the materials shall not 
fall from any height through the water, but be deposited in the 
allotted place in a compact mass ; otherwise the cement will be 
separated from the other ingredients and the strength of the 
work be seriously impaired. If the concrete is allowed to fall 
through the water its ingredients will be deposited in a series, 
the heaviest — the stone, at the bottom, and the lightest — the 
cement, at the top. A fall of even one foot causes an appreciable 
separation. 

A common method of depositing concrete under water is to 
place it in a V-shaped box of wood or plate iron, which is 
lowered to the bottom with a crane. The box is so constructed 
that on reaching the bottom a latch operated by a rope reaching 
to the surface can be drawn out, thus permitting one of the slop- 
ing sides to sw^iug open and allows the concrete to fall out. The 
box is then raised and refilled.- 

A long box or tube, called a tremie., is also used. It consists 
of a tube open at top and bottom built in detachable sections, 
so that the length may be adjusted to the depth of water. The 
tube is suspended from a crane or movable frame running on a 
track, by which it is moved about as the work progresses. The 
upper end is hopper-shaped, and is kept above the water . the 
lower end rests on the bottom. The tremie is filled in the begin- 
ning by placing the lower end in a box with a movable bottom, 
filling the tube, lowering all to the bottom, and then detaching 
the bottom of the box. The tube is kept full of concrete by 
more being thrown in at the top as the mass issues from the 
bottom. 

Concrete is also successfully deposited under water by enclos- 
ing it in paper bags and lowering or sliding them down a chute 
into place. The bags get wet and the pressure of the concrete 
soon bursts them, thus allowing the concrete to unite into a solid 
mass Concrete is also sometimes deposited under water by en- 
closing it in open-cloth bags, the cement oozing through the 
meshes sufticiently to \mite the whole into a single mass. 

Concrete should not be deposited in running water unless 
protected by one or other of the above- described methods; other- 
wise the cement will be washed out. 

Concrete deposited under water should not be rammed, but if 



ASPHALTiC COKCREtE 229 

necessary may be levelled with a rake or other suitable tool im« 
mediatel}^ after being deposited 

When concrete is deposited in water a pulpy, gelatinous fluid 
is washed from the cement and rises to the surface. This causes 
the water to assume a milky hue. The French engineers apply 
the term laitance to this substance. It is more abundant in salt 
water than in fresh. The theory of its formation is that the im- 
mersed concrete gives up to the water, free caustic lime, which 
precipitates magnesia in a light and spongy form> This precipi- 
tate sets very slowly, and sometimes scarcely at all, and its inter- 
position between the layers of concrete forms strata of separa- 
tion. The proportion of laitance is greatly diminished by using 
large immersion boxes, or a tremie, or paper or cloth bags. 

Asphaltic Concreta is composed of asphaltic mortar and 
broken stone in the proportion of 5 parts of stone to 3 parts of 
mortar The stone is heated to a temperature of about 250° F. 
and added to the hot mortar> The mixing is usually performed 
in a mechanical mixer. 

The material is laid hot and rammed until the surface is 
smooth. Care is required that the materials are properly heated, 
that the place where it is to be laid is absolutely dry and that the 
ramming is done before it chills or becomes set. The rammers 
should be heated in a portable tire. 



MASONRY. — PREPAKATIOK OF THE STORES. 



ni. Masonry. 

Classification of Masonry. 

Masonry is classified according to the nature of the material 
used, as *' stone masonry," "brick masonry," and "mixed ma- 
sonry," composed of stones and bricks. 

Stone masonry is classified (1) according to the manner in 
which the material is prepared, as : "rubble masonry," " squared- 
stone masonr}^" "ashlar masonry,'' "broken ashlar," and the 
combinations of these four kinds ; and (2) according to the man- 
ner in which the work is executed, as: " uncoursed rubble,*' 
"coursed rubble," **dry rubble," "regular-coursed ashlar," 
"broken- or irregular-coursed ashlar," " ranged work," "random 
ranged," etc. 

Preparation of the Stones 

Classification of the Stones. 

All the stones used in building are divided into three classes 
according to the finish of the surface, viz. : 1. Rough stones that 
are used as they come from the quarry. 2. Stones roughly squared 
and dressed. 3. Stones accurately squared and finely dressed. 

Unsquared Stones. — This class covers all stones which are 
used as they come from the quarry without other preparation than 
the removal of very acute angles and excessive projections from 
the general figure. 

Squared Stones. — This class covers all stones that are roughly 
S([uared and roughly dressed on beds and joints. The dressing is 
usually done with the face-hammer or -axe, or in soft stones with 
the tooth hammer. In gneiss, hard limestones, etc., it may be 
necessary to use the point. The distinction between this class and 
the third lies in the degree of closeness of the joints. Where the 
dressing on the joints is such that the distance between the gen- 
( nil planes of the surfaces cf adjoining stones is one half inch 
or more the stones properly belong to this class. 



MASONRY.— STONE-CUTTING. 231 

Three subdivisions of tbis class may be made, depending on the 
character of the face of the stones. 

(a) QuAiiRY-FACED or Rock-Faced stones are those whose 
faces are left untouched as they come from the quarry. 

(6) Pitched-faced stones are those on which the arris is 
clearly defined by a line beyond which the rock is cut away by 
the pitchiug-chisel, so as to give edges that are approximately 
true. 

(c) Drafted Stones are those on which the face is surrounded 
by a chisel-draft, the space inside the draft being left rough. Or- 
dinarily, however, this is done only on stones in which the cutting 
of the joints is such as to exclude them from this class. 

In ordering stones of this class the specifications should always 
state the width of the bed and end joints which ai-e expected, 
and also how far the surface of the face may project beyond the 
plane of the edge. In practice the projection varies between 1 inch 
and 6 inches. It should also be specified whether or not the faces 
are to be drafted. 

Cut Stones. — This class covers all squared stones with 
smoothly dressed beds and joints. As a rule, all the edges of cut 
stones are drafted, and between the drafts the stone is smoothly 
dressed. The face, however, is often left rough where construc- 
tion is massive. The stones of this class are frequently termed 
" dimension " stone or *' dimension " work. 



Stoiie-cutting. 

Dressing the Stones. —The stone-cutter examines the rough 
blocks as they come from the quarry in order to determine 
whether the block will work to better advantage as a header, a 
stretcher, or a corner-stone. Having decided for which purpose the 
stone is suited, he prepares to dress the bottom bed. The stone 
is placed with the bottom bed up, all the rough projections are 
removed with the hammer and pitchiug-tool, and approximately 
straight lines are pitched off around its edges ; then a chisel- 
draft is cut on all the edges. These drafts are brought to the 
same plane as nearly as practicable by the use of two straight- 
edges having parallel sides and equal widths, and the enclosed 
rough portion is then dressed down with the pitching-tool or 
point to the plane of the drafts. The entire bed is then ])ointcd 
down to a surface true to the straight-cdiie when applied in any 
direction — crosswise, lengthwise, and diigonally. 



532 MASOKRY. — STOKE-CITTTIKG. 

Lines are then marked on this dressed surface parallel and pi* 
peudicular to the face of the stone, enclosing as large a rectauglc 
as the stone will admit of being worked to, or of such dimensions 
as may be directed by the plan. 

The faces and sides are pitched off to these lines. A chisel- 
draft is then cut along all four edges of the face, and the face 
either dressed as required or left rock-faced. The sides are then 
pointed down to true surfaces at right angles to the bed. The 
stone is turned over bottom bed down, and the top bed dressed 
in the same manner as the bottom. It is important that the top 
bed be exactly parallel to the bottom bed in order that the stone 
may be of uniform thickness. 

Stones having the beds inclined to each other, as skew-backs, or 
stones having the sides inclined to the beds, are dressed by using 
a bevelled straight-edge set to the required inclination. 

Arch-stones have two plane surfaces inclined to each other ; 
these are called the beds. The upper surface or extrados is usually 
left rough ; the lower surface or intrados is cut to the curve of 
the arch. This surface and the beds are cut true by the use of a 
wooden or metal templet which is made according to the drawings 
furnished by the engineer or architect. 

Dressing Granite, 

The tools employed in dressing granite are the set, the spalling- 
hammer, the pean-hammer, the bush-hammer, the chisel, the 
bush-chisel, the point, and the hand-hammer. The set is used 
for dressing the edges of a block to a line. The spalling-hammer 
is sometimes used for taking off larger projections than can be 
dressed off with the set, but such projections are commonly 
taken off with wedges (or ''plugged off"). The point is used 
for roughing out the contour of surfaces. With the pean-hammer 
the projections left by the point are cut down. The bush-hammer 
imparts a finish according to the number of cuts employed. 
The chisel is used for finishing mouldings, for cutting drafts 
around rock-faced and pointed work, and for lettering and 
tracing. The bush-chisel is used for dressing portions of sur- 
faces not accessible with the bush-hammer. The set, point, and 
chisels are driven with the hand-hammer. 

The steps in the process of dressing a granite surface are : 1st, 
dressing the edges to a line with ^ho sot ; Od, roughing out the 
surface with the point ; 3d, cutLing down tlie irregularities left 



MASOKRY. — DRESSING GRANITE. 233 

by the point with the pean -hammer; and 4th, dressing down wiih 
the 4-cut, 6-cut, 8-cut, 10 cut, and 12-cut busb-hammers success- 
ively the irregularities left by each preceding tool. 

This process is carried out to different degrees for the different 
kinds of finished dressing, known as rock-faced work, pointed 
work, siugle-cut or pean-hammered work, and 4-cut, 6-cut, 8-cut 
10-cut, and 12-cut work. For pointed work there is usually a 
draft chiselled around the face, after which the space within is 
dressed to a level with the draft or is given a certain projection, 
and may be rough-pointed or fine-pointed. Rock-faced work 
is sometimes drafted. The bed and joint surfaces are dressed 
to a degree of fineness depending upon the closeness of the 
joint requried. 

The condition of the surface at the completion of any particular 
cut work should be such that each cut in the hammer traces a line 
its full length on the stone at every blow. The first cut should 
leave no unevenness exceeding one eighth of an inch, and each 
finer cut reduces the amount of unevenness ; and the 12-cut 
tshould leave no irregularities other than the indentations made 
by the impinging of the blades in the hammer upon the surface 
of the stone. The lines of the cuts are made to be vertical on 
exposed faces ; on the beds and unexposed surfaces they are made 
straight across in the direction which is most convenient. 

For fine and accurate work all the tools designated in the com- 
plete process are used, except that a 5-cut hammer is often substi- 
tuted for the 4-cut and the 6-cut hammers ; but some of the tools 
are ordinarily omitted, the 6-cut being made to follow the pean- 
hammer, the 10-cut to follow the 6-cut, etc. 

Sawing and cutting granite by machinery is used, but not 
extensively. 

Polishing Granite.— The surface of granite for polishing is 
prepared with the 10-cut or the 12-cut bush-hammer. The proc- 
ess of polishing consists in: 1st, rubbing with sand; 2d, with 
emery ; and 3d, with putty-powder. All these polishing materijils 
are put on with just sufiicient water to make a paste which is not 
gummy. The putty-powder is rubbed on with a felt-covered 
block to give the surface a gloss finish. The machine employed 
for polishing is iron wheels formed of several concentric rings. 



234 MASOKRY. — dressi:n^g san^dstone, etc. 



Oressiiig- Saudstoue, 

The steps in the process of cutting sandstone are similar to 
those in the process of cutting marble, except that the crandall 
takes the place of the tooth-chisel on large surfaces. The dia- 
mond-hammer is used after the crandall on some kinds of sand- 
stone, and the bush-hammer is used on hard, compact, argilla- 
ceous sandstones like the North River bluestone. 

Blocks of sandstone are sawed with gang-saws. Some sand- 
stones are so soft when first taken from the quarry that they can 
be sawed without the aid of sand. 

A rubbed surface is the finest finish of which sandstone is 
susceptible. The surface may be rubbed with sand alone, or 
with sand followed by grit. 

Slabs of. North River bluestone are planed, like slabs of slate, 
before they are rubbed. 

Dressing Limestone. 

The beds of limestone are usually smooth eoough to be used in 
ordinary masonry without dressing. The ends are jointed with 
the pitchiug-tool and point, and the faces are commonly dressed 
rock- face. Heavily bedded limestones are commonly sawed with 
gang-saws, and the various kinds of finish given the faces are 
rock-face, pointed, tooled, drove, or rubbed. Sometimes the 
looth-axe is used after the point, after that the axe-hammer, and 
then the diamond-hammer. 



Dressing Marble. 

The steps taken in the process of cutting marble are : lst» 
shaping up the block with the spalling-hammer and pitching- 
tool; 2d, roughing out the surface with the point; 3d, cutting 
down the projection left by the point with the tooth-chisel; and 
4th, cutting the surface smooth with the drove. 

The spalling-hammer is used for breaking off the larger pro- 
jections, ana the pitching-tool is used for dressing the edges to a 
line. Chisels having a bit more than one inch in width are 
called *• droves ", smaller sizes are called " tools." 

A fiuishea surface is usually drove, tooled, or polished. Rock- 
laced, pointed; and tooth-chiselled work is seldom employed. A 



MASONRY. — DRESSING SLATE. 235 

tooled surface is made with the chisel, and has a ridged or wavy 
appearance, due to the lines of indentations made by the tool. 
Machines are extensively employed for working marble. 

Polishing Marble. — Surfaces to be polished are finished 
with the ''drove." The steps involved in the process of polish- 
ing are: 1st, rubbing with coarse sand; 2d, with finer sand; 3d, 
with coarse grit; 4th, with finer grit; 5th, with pumice-stone; 
6th, polishing with Scotch bone; and 7th, glossiog with putty- 
powder, with sometimes the addition of oxalic acid. Water is 
applied in every step of the process. 

It is usually specified in contracts for polished work that no 
oxalic acid shall be used, because a more durable polish is 
obtained by the use of putty-powder alone. 

Small blocks are rubbed with sand on the rubbing-bed; other- 
wise machines similar to those used for polishing granite are 
used for applying the sand and putty-powder. The grit consists 
of spalls from a sand-rock which has a texture suitable for grind- 
stones. The grit and pumice-stone and Scotch bone are applied 
by hand. Each step in the process must eradicate all traces of 
the preceding step. All scratches must be removed from the 
surface before beginning the work of imparting the gloss finish. 

A dressed surface of most colored marbles will have cavities, 
which must be filled before the marble is polished. This filling 
is done with a wax made of shellac and colored with any non- 
oily substance ; it is applied with a red-hot strip of iron, and 
before the wax cools a little of the marble-dust is rubbed into it. 
The same material is also used for cemeutiug pieces of colored 
marble together. White marble cannot be successfully filled. 



Dressing Slate, 

Roofing-slate is prepared by splitting the blocks of slate 
as they come from the quarry. The splitter uses a broad, 
thin chisel. He splits the block of slate through the mid- 
dle, and continues to divide the pieces into equal halves until 
they are reduced to the required thinness. The edges of the 
block must be kept moist from the time the rock is taken from 
the quarry until it is split up. In some quarries the blocks split 
best from the side, and in others from the end, and in some qual- 
ities of sJate the splitting chisel may be driven in its whole length 
without danger of breaking the slate, while in others it is neces- 



236 MASONRY. — DRESSING SLATE. 

sary to lead tbe split by driving the chisel slightly all around the 
edges of the bl;)ck before driving it in at any one point. There 
are many other little peculiarities which need to be watcheii by 
the splitter, and almost every diifereiit quarry presents some 
characteristic features which modify the working of the slate. 

To trim slate by hand a straight- edged strip of iron or steel is 
fa^eued horizontally on one of the upper edges of a rectangular 
block about 18 inches in height; the trimmer lays the slate upon 
the block, allowing one of the irregular edges to project over the 
iron plate, and cutting it off by a chopping stroke with a heavy 
knife. In this manner he trims two edges at right angles to each 
other, and then marks out the other two edges with a measuring- 
stick before trimming them. The measuring-stick has a nail 
through one end and notches or steps toward the other end at 
distances from the point of the nail corresponding witfi the 
lengths and breadths of slates made. 

Machines operated by manual power are also used for trimming 
slates. 

For mantels, lavatories, and many other purposes slate is 
worked up principally b}^ machinery. The blocks are taken 
from the quarries to tlie slate-mills and there split into slabs 
about 2 inches in thickness and sawed into the required sizes 
with circular saws. The sawed slabs are planed with a planing 
machine like the machines used for planing iron. The planer- 
chisels vary in width from 2 to 6 inches, according to the softness 
of the slate. The slabs are finished by rubbing with sand and 
water. The rubbing-bed is a flat, circular piece of cast iron, from 
8 to 10 feet in diameter, revolving horizontally on a shaft. 

Slates do not receive a gloss polish, but if a finer surface is 
desired than that which can be given by the rubbing-bed it is 
rubbed by hand with fine sand or emery. 



METHODS OF Fliq^ISHII^G THE FACES OF CUT STOKE. 237 



Methods of Finisliing the Faces of Cut Stone. 

la architecture there are a great many ways in which the faces 
of cut stone may be dressed, but the following are those that will 
be usually met in engineering work: 

Rough- POINTED. — When it is necessary to remove an inch or 
more from the face of a stone it is done by the pick or heavy 
point until the projections vary from ^ to 1 inch. The stone is 
said to be rough-pointed. In dressing limestone and granite this 
operation precedes all others. 

Fine-pointed. — If a smoother finish is desired rough-pointing 
is followed by fine-pointing, which is done with a fine point. 
Fine-pointing is used only where the finish made by it is to be 
final, and never as a preparation for a final finish by another tool. 

Crandalled. — This is only a speedy method of pointing, the 
effect being the same as fine-pointing, except that the dots on 
the stone are more regular. The variations of level are about | 
inch and the rows are made parallel. When other rows at right 
angles to the first are introduced the stone is said to be cross- 
crandalled. 

Axed or Pean-hammered, and Patent-hammered.— These 
two vary only in the degree of smoothness of the surface which 
is produced. The number of blades m a patent hammer varies 
from 6 to 12 to the incli; and in precise specifications the number 
of cuts to the inch must be stated, such as 6-cut, 8-cut, 10-cut, 12- 
cut. The effect of axing is to cover the surface with chisel- 
marks, which are made parallel as far as practicable. Axing is a 
final finish. 

Tooth- AXED. — The tooth -axe is practically a number of points, 
and it leaves the surface of a stone in the same condition as fine- 
pointing. It is usually, however, only a preparation for bush- 
hammering, and the work is then done without regard to effect, 
so long as the surface of the stone is sufficiently levelled. 

Bush- HAMMERED. — The roughnesses of a stone are pounded off 
by the bush-hammer, and the stone is then said to be " bushed." 
This kind of finish is dangerous on sandstone, as experience has 
shown that sandstone thus treated is very apt to scale. In dress- 
ing limestone which is to have a bush- hammered finish the 
usual sequence of operation is (1) rough-pointing, (2) tooth-axing, 
and (3) bush-hammering. 



238 MASONUY. — TOOLS USED i:Nr STONE-CUTTING. 

Rubbed.— In dressing sandstone and marble it is very common 
to give the stone a plane surface at once by use of the stone-saw. 
Any roughnesses left by the saw are removed by rubbing with 
grit or sandstone. Such stones, therefore, have no margins. 
They are frequently used in architecture for string-courses, lin- 
tels, door- jambs, etc.; and they are also well adapted for use in 
facing the wails of lock-chambers and in other positions where 
a stone surface is liable to be rubbed by vessels or other moving 
bodies. 

Diamond Panels. — Sometimes the space between the margins 
is sunk immediaU'ly adjoining them, and then rises gradually 
until the four planes form an apex at the middle of the panel. In 
general such panels are called diamond panels, and the form just 
described is called a sunk diamond panel. When the surface of 
the stone rises gradually from the inner lines of the margins to 
the middle of the panel it is called a raised diamond panel. 
Both kinds of finish are common on bridge-quoins and similar 
work. 

Tools used in Stone-cutting. 

The Double FACE Hammer is a heavy tool, weighing from 20 
to 30 pounds, used for roughly shaping stones as they come from 
the quarry and for knocking off projections. This is used for 
only the roughest work. 

The Face-hammer has one blunt and one cutting end, and is 
used for the same purpose as the double-face hammer where less 
weight is required. The cutting end is used for roughly squar- 
ing stones preparatory to the use of finer tools. 

The Cavil has one blunt and one pyramidal or pointed end, 
and weighs from 15 to 20 pounds. It is used in quarries for 
roughly shaping stone for transportation. 

The Pick somewhat resembles the pick used in digging, and 
is used for rough-dressing, mostly on limestone and sandstone. 
Its length varies from 15 to 24 inches, the thickness at the eye 
being about 2 inches. 

The Axe or Pean-hammer has two opposite cutting edges. It 
is used for making drafts around the arris or edge of stones, and 
in reducing faces, and sometimes joints, to a level. Its length is 
about 10 inches and the cutting edge about 4 inches. It is used 
after the point and before the patent hammer. 

The Tooth- AXE is like the axe, except thatjts cutting edges are 
divided into teeth, tlie number of whichVaries with the kind of 



MASOi^^KY. — TOOLS USED li^ STONE-CUTTING. 239 

work required. This tool is not used in granite- and gneiss- 
cutting. 

The Bush-hammer is a square prism of steel, whose ends are 
cut into a number of pyramidal points. The length of the ham- 
mer is from 4 to 8 inches and the cutting face from 2 to 4 inches 
square. The points vary in number and in size with the work 
to be done. One end is sometimes made with a cutting edge 
like that of the axe. 

The Grand ALL is a malleable-iron bar about 2 feet long 
slightly flattened at one end. In this end is a slot 3 inches long 
and f inch wide. Through this slot are passed ten double- 
headed points of i-inch square steel 9 inches long, which are 
held in place by a key. 

The Patent Hammer is a double-headed tool so formed as to 
hold at each end a set of wide thin chisels. The tool is in two 
parts, which are held together by the bolts which hold the 
chisels. Lateral motion is prevented by four guards on one of 
the pieces. The tool without the teeth is 5^ X 2i X li inches. 
The teeth are 2| inches wide; their thickness varies from yV to J 
of an inch. This tool is used for giving a finish to the surface of 
stones. 

The Hand-hammer, weighing from 2 to 5 pounds, is used in 
drilling holes and in pointing and chiselling the harder rocks. 

The Mallet is used where the softer limestones and sand- 
stones are cut. 

The Pitching-chisel is usually of IJ-inch octagonal steel, 
spread on the cutting edge to a rectangle of f X 2^ inches. It is 
used to make a well-defined edge to the face of a stone, a line 
being marked on the joint surface, to which the chisel is applied 
and the portion of the stone outside of the line broken off by a 
blow with the hand-hammer on the head of the chisel. 

The Point is made of round or octagonal steel from | to 1 
inch in diameter. It is made about 12 inches long, with one end 
brought to a point. It is used until its length is reduced to 
about 5 inches. It is employed for dressing off the irregular 
surface of stones, either for a permanent finish or preparatory 
to the use of the axe. According to the hardness of the stone, 
either the hand-hammer or the mallet is used with it. 

The Chisel is of round steel of J to | inch diameter and about 
10 inches long, with one end brought to a cutting edge from J 
inch to 2 inches wide; is used for cutting drafts or margins on 
the face of stones. 



240 DEFINITION OF TERMS USED IN STONE-CUTTING. 

The Tooth-chisel is the same as the chisel except that the 
cutting edge is divided into teeth. It is used only on marbles 
and sandstones. 

The Splitting-chisel is used chiefly on the softer stratified 
stones, and sometimes on fine architectural carvings in granite. 

The Plug, a truncated wedge of steel, and the feathers of half- 
round malleable iron, are used for splitting unstratified stone. 
A row of holes is made with the drill on the line on which the 
fracture is to be made; in each of these holes two feathers are 
inserted, and the plugs lightly driven in between them. The 
plugs are then gradually driven home by light blows of the 
hand-hammer on each in succession until the stone splits. 

Machine-tools. — In all large stone-yards machines are used 
to prepare the stone. There is a great variety in their form, but 
since the kind of dressing never takes its name from the machine 
which forms it, it will be neither necessary nor profitable to 
attempt a description of individual machines. They include. 
stone-saws, stone-cutters, stone-planers, stone-grinders, stone ► 
polishers, etc. 

Definition of Terms used in Stone-cutting. 

Axed : Dressed to a plane surface with an axe. 

Boasted or Chiselled : Having face wrought with a chise) 
or narrow tool. 

Broached : Dressed with a ** punch " after being droved. 

Bush-hammered : Dressed with a bush-hammer. 

Crandalled : Wrought to a plane with a crandall. 

Deadening ; The crushing or crumbling of a soft stone under 
the tools while being dressed. 

Dressed Work : That which is wrought on the face; also 
applied to stones having the joints wrought to a plane surface, 
but not "squared." 

Drafted : Having a narrow chisel- draft cut around the face 
or margin. 

Droved, Stroked : Wrought with a broad chisel or hammer 
in parallel flutings across the stone from end to end. 

Hammer-dressed : Worked with the hammer. 

Herring-bone . Dressed in angular flutings. 

Nigged or Nidged : Picked with a pointed hammer or cavil 
to the desired form. 

Patent-hammered : Dressed with a patent hammer. 



MASONRY.— IN^SPECTION" OF CUT STOKE. 241 

Picked : Reduced to an approximate plane with a pick. 

Pitched : Dressed to the neat lines or edges with a pitching- 
chisel. 

Plain : Rubbed smooth to remove tool-marks. 

Pointed : Dressed with appoint or very narrow tool. 

Polished : Rubbed down to a reflecting surface. 

Prison: Having surfaces wrought into holes. 

Random-tooled or Dkqved : Cut with a broad tool into 
irregular flutings. 

RocK-FACED, Quarry-faced, Rough ; Left as it comes from 
the quarry. It may be drafted or pitched to reduce projecting 
points on the face to given limits. 

Rubbed : See Plain. 

Rustic, Rusticated : Having the faces of stones projecting 
beyond the arrises, which are bevelled or drafted. The face may 
be dressed in any desired manner. 

ScABBLE : To dress off the angular projections of stones for 
rubble masonry with a stone-axe, or hammer. 

Smooth : See Plain. 

Square-droved : Having the flutings perpendicular to the 
lower edge of the stone. 

Striped : Wrought into parallel grooves with a point or punch. 

Stroked : See Droved. 

Tooled : Wrought to a plane with an inch tool. See Droved. 

Toothed : Dressed with a tooth-chisel.. 

Vermiculated, Worm- work : Wrought into veins by cutting 
away portions of'the face. 

Inspection of Cut Stone. 

< The stone-cutter's shed should be frequently visited and the 
stones in hand examined (1) to discover any defects which have 
been overlooked in the examination of the rough stone; (2) for 
correctness of the dimensions; (3) character and quality of the 
workmanship. The dressing of the bed-joints should receive special 
attention. The surface of the bed should be true to the straight- 
edge placed in every direction across it. The practice of stone- 
cutters is to leave the beds a little *' slack," i. e., concave. This 
should not be permitted without instructions from the chief. 
Stones with concave beds are liable to have their edges ^plit off 
by the pressure, which, instead of being distributed over the 
whole area of the stone, is concentrated at the edges. The joints 



242 MASONRY.— INSPECTION OF CUT STONE. 

formed by such stones are said to be flushed. They are difficult 
of detection after the masonry is built, and are often executed by 
design in order to give the face of the masonry a neat appearance, 
and therefore their occurrence must be guarded against by careful 
inspection of the progress of the stone-cutting. 

If any part of the surface of the bed projects beyond the 
plane of the chisel- draft that projecting part will have to bear an 
undue share of the pressure, which will be concentrated upon it, 
and the joint formed by such stones will gape at the edges, 
forming what is called an open joint. 

When the stone has been dressed so that all the small ridges on 
its surface are in one plane with the chisel-drafts the pressure Is 
distributed with a near approach to uniformity for the mortar 
serves to transmit it to the furrows between the ridges. 

Great smoothness is not desirable in the joints of masonry in- 
tended for strength and stability a moderate degree of roughness 
adds to the resistance to sliding and to the adhesion of the 
mortar. 

Moulded and rubbed work requires close watching, that the 
pieces may not be distorted or rubbed into hollow or concave 
patches. 

Patched Stones —Stones accidentally broken after being cut 
should not be allowed to be patched and used. The practice of 
patching is frequently followed in granite and other brittle stones 
The broken pieces are glued in with melted shellac. In dry 
weather and while still fresh from the tool such patches are 
hardly noticeable unless near the eye, therefore they should be 
closely looked for; but when the stone is wet by rain the patch 
becomes conspicuous, and as the shellac is slowly destroyed the 
piece may eventually drop out. 

Ashlar Facing.— The dressing of the face-stones which are to 
be backed with squared stones must be watched very closely, for 
the workmen seldom take the pains necessary to dress the beds 
and joints accurately; on the contrary, to obtain what are termed 
'* close joints" they dress the joints with accuracy a few inches 
only from the outward surface, and then chip away the stone 
towards the back, so that when the block is set it will be in 
contact with the adjacent stones only throughout this very small 
extent of bearin*^ surface. This practice is objectionable from 
every point of view; for, m the first place, it gives an inadeqiiate 
extent of bearing surface, which, being generally insufficient to 
resist the pressure thrown on it, causes the block to splinter oil 



MASOKRY.— MORTAR, 243 

and, in the second place, to give the block its proper set it has to 
be propped up by small bits of stone, an operation called ''spal 
ling up," '* pinning up/' or underpinning, and these props, cans 
ing the pressure on the block to be thrown on a few points of the 
lower surface instead of being equally diffused over it, expose 
the stone to crack. 

Mortar. 

Mortar is made by mixing lime or cements with clean sand 
and adding just sufficient water to make a plastic mass. The pro- 
portion of sand depends upon the character of the lime or 
cement. 

Cement Mortar — In mixing cement mortar the cement and 
sand are first thoroughly mixed dry. the water then added, and 
the whole worked to a uniformly plastic condition. 

The quality of the mortar depends largely upon the thorough- 
ness of the mixing, the great object of which is to so thoroughly 
incorporate the ingredients that no two grains of sand shall lie 
together without an intervening layer or film of cement To ac- 
complish this the cement must be uniformly distributed through 
the sand during the dry mixing. 

The mixers usually fail to thoroughly intermix the dry cement 
and sand, and to lighten the labor of the wet mixing they will 
give an overdose of water 

In hand mixing there is great liability of errors in measuring 
out correct and uniform proportions of the prescribed materials 

Mortar-men make mistakes which generally happen to be 
against the proper quantity of cement 

Packed cement when measured loose increases in volume to 
such an extent that a nominal 1 to 3 mortar is easily changed to 
an actual 1 to 4. When the specifications prescribe measure by 
volume the inspector should obtain definite directions from the 
engineer as to the manner in which the materials are to be meas- 
ured, i. e., packed or loose. 

The quantity of sand will also vary according to whether it is 
measured in a wet or dry condition, packed or loose. 

On work of sufficient importance to justify some sacrifice of 
convenience the sand and cement should be proportioned by 
weight instead of by volume. 

- In mixing by hand a platform or box should be used; the sand 
and cement should be spread in layers with a layer of sand at the 



244 MASOKRY.— MORTAR. 

bottom, then turned and mixed with shovels until a thorough in 
corporation is effected. The dry mixture should then be spread 
out, a bowl-like depression formed in the centre, and all the water 
required poured into it. The dry material from the outside of 
the basin should be thrown in until the water is taken up and 
then worked into a plastic condition, or the dry mixture may be 
shovelled to one end of the box and the water poured into the 
other end. The mixture of sand and cement is then drawn 
down with a hoe, small quantities at a time, and mixed with the 
water until enough has been added to make a good stiff mortar 

In order to secure proper manipulation of the materials on the 
part of the workmen it is usual to require that the whole mass 
shall be turned over a certain number of times with the shovels, 
both dry and wet. 

The mixing wet with the shovels must be performed quickly 
and energetically. The paste thus made should be vigorously 
worked with a hoe for several minutes to insure an even mixture. 
The mortar should then leave the hoe clean when drawn out of 
it, and very little should stick to the steel 

A large quantity of cement and sand should not be mixed dry 
and left to stand a considerable time before using; as the moisture 
in the sand will to some extent act upon the cement, causing a 
partial setting. 

Upon large works mechanical mixers are frequently employed 
with the advantage of at once lessening the labor of manipulating 
the material and insuring good work. 

The proportion of sand to cement depends upon the nature of 
the work and the necessity for the development of streugth or 
imperviousness in the mortar. The relative quantities of sand and 
cement should also depend upon the nature of the sand; fine sand 
requires more cement than coarse This element is, however., not 
usually given the consideration it demands. (See Table 58 ) 

The proportions required by the New York Building Laws of 
1896 are as follows : 

*' Cement mortars shall be made of sand and cement in the 
proportion of not more than three parts of sand to one part of 
cement. 

* ' Lime mortar shall be made of not more than four parts of 
sand to one part of lime, and shall not be used before being thor- 
oughly slaked, 

"Cement and lime mortar shall be made of one part of lime, 
one part of cement, and three parts of sand to each." 



MASONllY, —MORTAR. 



345 



Table 58. 

AMOUNT OF CEMENT AND SAND REQUIRED FOR ONE CUBIC 
YARD OF MORTAR. 



Composition 


of Mortar by 


Cement * 




Volumes. 


Number of Barrels. 


Sand. 










Cement. 


Sand. 


Portland or 

Ulster County 

Rosendale, 


Western 
Rosendale. 


Cubic Yards. 


1 





7.14 


6.43 


0.00 


1 


1 


4,16 


3.74 


58 


1 


2 


2.85 


2.57 


0.80 


1 


3 


2.00 


1.80 


0.90 


1 


4 


1 70 


1.53 


0.95 


1 


5 


1.25 


1.13 


0.97 


1 


6 


1.18 


1.06 


0.98 






Cement.. Number of Pounds.t 




1 





2675 


2140 


00 


1 


1 


1440 


1150 


0.67 


1 


2 


900 


720 


0.84 


1 


3 


675 


540 


0.94 


1 


4 


525 


420 


98 


1 


5 


425 


340 


0.99 


1 


6 


355 


285 


1.00 



* Packed cement and loose sand, 
t Loose cement and loose sand. 

Sand for MortaRc —The sand used mxcst he cleaU; that is, free 
from clay, loam, mud. or organic matter; sharp, that is> the grains 
must be angular and not rounded as those from the beds of rivers 
and the seashore; coarse, that is, it must be large-grained, but 
not too uniform in size 

The best sand is that in which the grains are of different sizes* 
the more uneven the sizes the smaller will be the amount of 
voids, and hence the less cement required 

Water for Mortar. —Quality.— The water employed for 
mortar should be fresh and clean, free from mud and vegetable 
matter. 

Salt water may be used, but with seme natural cements it may 
retard the setting, the chloride and sulphate of magnesia being 
the principal retarding elements. Less sea-water than fresh will 
be required to produce a given consistency 



246 MASOKRY.— MORTAR. 

Quantity. — The quantity of water to be used ia mixing 
mortar can be determined only by experiment in each case. It 
depends upon the nature of the cement, upon that of the sand 
and of the water, and upon the proportions of sand to cement, 
and upon the purpose for which the mortar is to be used. 

Fine sand requires more water than coarse to give the same 
consistency. Dry sand will take more water than that which is 
moist, and sand composed of porous material more than that 
which is hard. As the proportion of sand to cement is increased 
the proportion of water to cement should also increase, but in a 
much less ratio. 

The amount of water to be used is such that the mortar when 
thoroughly mixed shall have a plastic consistency suitable for 
the purpose for which it is to be used. 

The consistency of mortar for masonry is such that it will 
stand in a pile and not be fluid enough to flow. For concrete 
the consistency required is such that if a ball of mortar be formed 
in the hand and allowed to fall through a height of about 20 
inches it will neither lose its form nor crack; the ball should not 
be wet enough to stick to the hand. 

In all cases the proper quantity of water should first be deter- 
mined by experiment upon small quantities of the materials, and 
afterwards, in preparing the mortar for use, the required quan- 
tity should each time be added by measurement. 

The addition of water, little by little, or from a hose, should 
not be allowed. 

Workmen, as a rule, add an excess of water for the purpose of 
reducing the labor of mixing. 

From numerous experiments it has been found that, as a gen- 
eral rule, a proportion of 1 part of water to 3 parts of cement 
by measure, or 1 to 3^ by weight, is the best, both as regards 
convenience of mixing and results. 



MASONRY. — EFFECT OF RETEMPERING MORTAR. 247 



EflPect of Retempering Mortar. 

Masons very frequently mix mortar in considerable quantities, 
and if the mass becomes stiffened before being used, by the set- 
ting of the cement, add water and work it again to a soft or 
plastic condition. After this second tempering the cement is 
much less active than at first, and will remain for a longer time 
in a workable condition. 

This practice is condemned by engineers, and is not usually 
allowed in good engineering construction. Only sufficient quan- 
tity of mortar should he mixed at once as may be used before the 
cement takes the initial set. Bejeci all mortar thai has set before 
being placed in the work. 

The mortar is placed on the work with the intention of its 
being used before it has taken its initial set. But masons like it 
extremely plastic, and before their mortar-boards are emptied 
they will make frequent calls to "temper up"; more water is 
added with remixing, and if oversight is relaxed the prescribed 
time of using it will have elapsed, and a diluted, weakened, and 
second-set material will have been used. Masons are so imbued 
with the belief that the '* second set" is desirable and harmless 
that they will use every endeavor to obtain it. They will claim 
that it was permitted on some other notable work, and that it is 
unreasonable to prevent it, that they can do more work and with 
more ease, etc., etc. It is true that brick can be laid with more 
ease and rapidity with such mortar than when it is in proper 
condition; but it has been found that mortar that has taken its 
initial set and is remixed, with the addition of more water, 
loses about one half the tensile strength due to it if used in 
proper condition. 

Freezing of Mortar.* — **It does not appear that common 
lime mortar is seriously injured by freezing, provided it remains 
frozen until it has fully set. The freezing retards, but does not 
entirely suspend, the setting. Alternate freezing and thawing 
materially damages the strength and adhesion of lime mortar. 

• ' Although the strength of the mortar is not decreased by freez- 
ing, it is not always [permissible to lay masonry during freezing 
weather; for example, if, in a thin wall, the mortar freeze before 
setting and afterwards thaw on one side only, the wall may 
settle injuriously. 

"^ Baiter's ''Masonry Construction." 



248 MASONRY.— ASHLAR MASONRY. 

' * Mortar composed of one part Portland cement and three parts 
sand is entirely uninjured by freezing and thawing. 

** Mortar made ot cements of tlie Rosendale type^ in any propor- 
tion, is entirely ruined by freezing and thawing.""^ 

Mortar made of overclayed cement (which condition is indi- 
cated by its quicker setting), of either the Portland or Rosendale 
type, will not withstand the action of frost as well as one con- 
taining less clay, for since the clay absorbs an excess of water, it 
gives an increased effect to the action of frost. 

In making cement mortar during freezing weather it is cus- 
tomary to add salt or brine to the water with which it is mixed. 
The ordinary rule is: Dissolve 1 pound of salt in 18 gallons of 
water when the temperature is at 32° F., and add 1 ounce of salt 
for each degree of lower temperature. 

The use of salt, and more especially of sea- water, in mortar is 
objectionable, since the accompanying salts usually produce 
efflorescence. 

The practice of adding hot water to lime mortar during freez- 
ing weather is undesirable. When the very best results are 
sought the brick or stone should be warmed— enough to thaw off 
any ice upon the surface is sufficient — before being laid. They 
may be warmed either by laying them on a furnace, or by sus- 
pending them over a slow fire, or by wetting with hot water. 



Ashlar Masonry. 

Ashlar masonry consists of blocks of stone cut to regular 
figures, generally rectangular, and built in courses of uniform 
height oi rise, which is seldom less than a foot. 

Size of the Stones.— In order that the stones may not be 
liable to be broken across no stone of a soft material, such as the 
weaker kinds of sandstone and granular limestone, should have a 
length greater than 3 times its depth or rise; in harder mateiials 
the length may be 4 or 5 times the depth. The breadth in soft 
materials may range from 1^ to double the depth; in hard mate- 
rials it may be 3 times tlie depth. 

Laying the Stone. — The bed on which the stone is to be laid 
should be thoroughly cleansed from dust and well moistened witli 
water. A thin bed of mortar should then be spread evenly over 
it, and the stone, the lower bed of which has been cleaned and 

♦Trans. Am. Soc. of C. E., Vol. XVI. pp. 79-84. 



MASONRY. — ASHLAR MASONJIY. 249 

moistened, raised into position, and lowered first upon one or 
two strips of wood laid upon the mortar-bed; then, by the aid of 
the pinch-bar, moved exactly into its place, truly plumbed, the 
strips of wood removed, and the stone settled in its place and 
levelled by striking it with wooden mallets. In using bars and 
rollers in handling cut stone the mason must be careful to protect 
the stone from injury by a piece of old bagging, carpet, etc. 

In laying "rock-faced " work the line should be carried above 
it, and care must be taken that the work is kept plumb with the 
cut margins of the corners and angles. 

The Thickness of Mortar in the joints of well executed 
ashlar masonry should be about J of an inch, but it is usually 
about |. 

Amount of Mortar. — The amount of mortar required for 
ashlar masonry varies with the size of the blocks, and also with 
the closeness of the dressing. With |- to ^-inch joints and 12- to 
20-inch courses there will be about 2 cubic feet of mortar per 
cubic yard ; with larger blocks and closer joints there will be 
about 1 cubic foot of mortar per yard of masonry. Laid in 1 to 
2 mortar, ordinary ashlar will require J to i of a barrel of 
cement per cubic yard of masonry. 

Bond of Ashlar Masonry. — No side- joint in any course 
should be directly above a side- joint in the course below ; but the 
stones should overlap or hreak joint to an extent of from once to 
once and a half the depth or rise of the course. This is called the 
hond of the masonry; its effect is to cause each stone to be supported 
by at least two stones of the course below, and assist in support- 
ing at least two stones of the course above ; and its objects are 
twofold : first, to distribute the pressure, so that inequalities of 
load on the upper part of the structure, or of resistance at 
the foundation, may be transmitted to and spread over an 
increasing area of bed in proceeding downwards or upwards, 
as the case may be ; and secondly, to tie the structure to- 
gether, or give it a sort of tenacity, both lengthwise and from 
face to back, by means of the friction of the stones where they 
overlap. The strongest bond in ashlar masonry is that in 
which each course at the face of the wall contains a header and 
a stretcher alternately, the outer end of each header resting on 
the middle of a stretcher of the course below, so that rather more 
than one third of the area of the face consists of ends of headers 
This proportion may be deviated from when circumstances re- 
quire it ; but in every case it is advisable that the ends of headers 



250 MASONRY. — BROKEN ASHLAR. 

should not form less than one fourth of the whole area of the face 
of the wall. 

Squared-stone Masonry. 

The distinction between squared-stone masonry and ashlar 
lies in the churacter of the dressing and the closeness 
of the joints. In this class of masonry the stones are roughly 
squared and roughly dressed on beds and joints, so that 
the width of the joints are half an inch or more. The 
same rules apply to breaking joint, and to the proportions 
which the lengths and breadths of the stones should bear to their 
depths, as in ashlar ; and as in ashlar, also, at least one fourth 
of the face should consist of headers, whose length should be 
from three to five times the depth of the course. 

Amount of Moktar. — The amount of mortar required for 
squared-stone masonry varies with the size of the stones and with 
the quality of the masonry ; as a rough average one sixth to one 
quarter of the mass is mortar. When laid in 1 to 2 mortar from 
J to I of a barrel of cement will be required per cubic yard of ^ 
masonry. 

Broken Ashlar, 

Broken ashlar consists of cut stones of unequal depths 
laid in the wall without any attempt at maintaining courses 
of equal rise or the stones in the same course of equal depth. 
The character of the dressing and the closeness of the joints 
may be the same as in ashlar or squared-stone masonry, 
depending upon the quality desired. The same rules apply to 
breaking joint, and to the proportions which the lengths and 
breadths of the stones should bear to their depths, as in ashlar ; 
and as in ashlar, also, at least one fourth of the face of the wall 
should consist of headers. 

Amount of Mortar. — The amount of mortar required when 
laid in 1 to 2 mortar will be from | to 1 barrel per cubic yard 
of maso»ry, depending upon the closeness of the joints. 



MASONBY. — RUBBLE MASONRY. 251 



Kubble Masonry. 

Masonry composed of unsquared stones is called rubble. This 
class of masonry covers a wide range of construction, from the 
commonest kind of dry-stone work lo a class of work composed of 
large stones laid in mortar. It comprises two classes : (1) uncoursed 
rubble, in which irregular-shaped stones are laid without any at- 
tempt at regular courses, and (2) coursed rubble, in which the 
blocks of unsquared stones are levelled off at specified heights to 
an approximately horizontal surface. Coursed rubble is often 
built in random courses; that is to say, each course rests on a 
plane bed, but is not necessarily of the same depth or at the same 
level throughout, so that the beds occasionally rise or fall by 
steps. Sometimes it is required that the stone shall be roughly 
shaped with the hammer. 

In buildiDg rubble masonry of any of the classes above men- 
ioned the stone should be prepared by knocking off all the weak 
ngles of the block. It should be cleansed from dust, etc., and 
moistened before being placed on its bed. Each stone should be 
firmly imbedded in the mortar. Care should be taken not only 
that each stone shall rest on its natural bed, but that the sides par- 
allel to that natural bed shall be the largest, so that the stone may 
lie flat, and not be set on edge or on end. However small and ir- 
regular the stones, care should be taken to break joints. Side-joints 
should not form, an angle with the bed-joint sharper than 60**. 
The hollows or interstices between the larger stones must be fi.lled 
with smaller stones and carefully bedded in mortar. 

One fourth part at least of the face of the wall should consist 
of 5(??it?-stones extending into the wall a length of at least 3 to 5 
times their depth, as in ashlar. 

Amount of Mortar required. — If rubble masonry is com- 
posed of small and irregular stones about J of the mass will con- 
sist of mortar ; if the stones are larger and more regular ^ to :^ 
will be mortar. Laid in 1 to 2 mortar, ordinary rubble requires 
f roB^ i to 1 barrel of cement per cubic yard of masonry. 



252 MASOKRY. — INSPECTION OF RUBBLE MASONRY. 



Inspection of Rubble Masonry. 

The construction of rubble masonry requires constant watchful- 
ness on the part of the inspector to see that the preceding rules 
are observed, and especially that the interior of the wall contains 
neither empty hollows nor spaces filled wholly with mortar or with 
rubbish where pieces of stone ought to be inserted, and that each 
stone is laid flat on its natural bed. Masons are very apt to set thin 
broad stones on their narrow edges so as to show a good face. The 
practice is injurious to the wall, for it exposes the bed of the stone 
to the destroying action of the atmosphere, and decreases the 
strength of the wall through lack of bonding. 

See that the headers or bond-stones are really what they profess 
to be, and not thin stones set on edge at the face of the wall. 

In bonding it is much better that many stones should reach 
two thirds across the wall alternately from the opposite faces than 
that there should be a few through stones extending the whole 
thickness of the wall. The bond-stones should not be directly 
over one another, but should be staggered. 

Very long stones should not be used in the face ; it is better to 
break them into two or more shorter ones. 

The excessive use of spalls under large stones should not be al- 
lowed ; the irregularities should be knocked off and the stones 
roughly bedded. 

A fault to be carefully guarded against is that of making the 
wall consist of two thin faces or sides with through bond-stones 
laid across to bind them together, the core being filled in with 
mortar and small stones. 

The placing of nigger-heads (field-stones or boulders from which 
the natural rounded surface has not been taken off) must not be 
permitted. 

A small steel rod is a very useful implement for detecting the 
defects in rubble masonry by probing the vertical joints. 



MASO]^RY, — ASHLAR BACKED WITH RUBBLE. 253 



Ashlar backed with Rubble. 

In this class of masonry the stones of the ashlar face should 
have their beds and joints accurately squared and dressed with the 
hammer or the points, according to the quality desired, for a 
breadth of from once to twice (or on an average once and a half) 
the depth or rise of the course, inwards from the face; but the 
backs of these stones may be rough. The proportion and length 
of the headers should be the same as in ashlar, and the *' tails" 
of these headers, or parts which extend into the rubble backing, 
may be left rough at the back and sides; but their upper and lower 
beds should be hammer-dressed to the general plane of the beds 
of the course. These tails may taper slightly in breadth, but 
should not taper in depth. 

The rubble backing built in the manner described under 
Rubble Masonry should be carried up at the same time with the 
face-work, and in courses of the same rise, the bed of each course 
being carefully formed to the same plane with that of the facing. 

General Rules to be observed in Ttaying All 
Classes of Stone Masonry. 

I. Build the masonry, as far as possible, in a series of courses, 
perpendicular, or as nearly so as possible, to the direction of the 
pressure which they have to bear, and by breaking joints avoid 
all long continuous joints parallel to that pressure. 

IL Use the largest stones for the foundation-course. 

III. Lay all stones which consist of layers in such a manner 
that the principal pressure which they have to bear shall act in a 
direction perpendicular, or as nearly so as possible, to the direc- 
tion of the layers. This is called laying the stone on its natural 
bed, and is of primary importance for strength and durability. 

IV. Moisten the surface of dry and porous stones before bed- 
ding them, in order that the mortar may not be dried too fast and 
reduced to powder by the stone absorbing its moisture. 

V. Fill every part of every joint and all spaces between the 
stones with mortar, taking care at the same time that such spaces 
shall be as small as possible. 

yi. The rougher the stones the better the mortar should be. 
The principal object of the mortar is to equalize the pressure ; 
and the more nearly the stones are dressed to closely fitting sur- 



254 MASONRY.— J3UICK MASONRY. 

faces the less important is the mortar. Not infrequently this 
rule is exactly reversed ; i. e., the finer the dressing the better the 
quality of the mortar used. 

All projecting courses, such as sills, lintels, etc., should be cov- 
ered with boards, bagging, etc., as the work progresses to protect 
them from injury and mortar-stains. 

When setting cut stone a pailful of clean water should be kept 
at hand, and when any fresh mortar comes in contact with the 
face of the work it should be immediately washed off. 

Brick Masonry. 

General Rules to be observed in Building with Bricks. 
— 1. To reject all misshapen and unsound bricks. 

3. To cleanse the surface of each brick, and to wet it thorough- 
ly before laying it, in order that it may not absorb the moisture 
of the mortar too quickly. 

3. To place the beds of the courses perpendicular, or as nearly 
perpendicular as possible, to the direction of the pressure which 
they have to bear ; and to make the bricks in each course break 
joint with those of the courses above and below by overlapping 
to the extent of from one quarter to one half of the length of a 
brick. (For the style of bond used in brick masonry see under 
Bond in list of definitions ) 

4. To fill every joint thoroughly with mortar. 

Brick should not be merely laid, but every one should be 
rubbed and pressed down in such a manner as to force the mortar 
into the pores of the bricks and produce the maximum adhesion ; 
with quick-setting cement this is still more important than with 
lime mortar. For the best work it is specified that the brick 
shall be laid with a *' shove-joint," that is, that the brick shall 
first be laid so as to project over the one below, and be pressed 
into the mortar, and then be shoved into its final position. 

Bricks should be laid in full beds of mortar, filling end- and 
side-joints in one operation. This operation is simple and easy 
with skilful masons — if they will do it — but it requires persist- 
ence to get it accomplished. Masons have a habit of laying brick 
in a bed of mortar leaving the vertical joints to take care of them- 
selves, throwing a little mortar over the top beds and giving a 
sweep with the trowel which more or less disguises the open 
joint below. They also have a way after mortar has been suffi- 
ciently applied to the top bed of brick to draw the point of their 



MASONRY. — BRICK MASONRY. 255 

trowel through it, making, an open channel with only a sharp 
ridge of mortar on each side (and generally throwing some of it 
overboard), so that if the succeeding brick is taken up it will 
show a clear hollow, free from mortar through the bed. This 
enables them to bed the next brick with more facility and avoid 
pressure upon it to obtain the requisite thickness of joint. 

With ordinary interior work a common practice is to lay brick 
with i' and f-inch mortar-joints : an inspector whose duty it is to 
keep joints down to J or | inch will not have an enviable task. 

Neglect in wetting the brick before use is the cause of most of 
the failures of brickwork. Bricks have a great avidity for 
water, and if the mortar is stiff and the bricks dry they will 
absprb the water so rapidly that the mortar will not set properly, 
and will crumble in the fingers when dry. Mortar is sometimes 
made so thin that the brick will not absorb all the water. This 
practice is objectionable ; it interferes with the setting of the 
mortar, and particularly with the adhesion of the mortar to the 
brick. Watery mortar also contracts excessively in drying (if it 
ever does dry), which causes undue settlement and, possibly, 
cracks or distortion. 

The bricks should not be wetted to the point of saturation, or 
they will be incapable of absorbing any of the moisture from the 
mortar, and the adhesion between the brick and mortar will be 
weak. 

The common method of wetting brick by throwing water from 
buckets or spraying with a hose over a large pile is deceptive , 
the water reaches a few brick on one or more sides and escapes 
many. Immersion of the brick for from 3 to 8 minutes, depend 
ing upon its quality, is the only sure method to avert the evil 
consequences of using dry or partially wetted brick. 

Strict attention must be paid to have the starting course level, 
for the bricks being of equal thickness throughout, the slightest 
irregularity or incorrectness in it will be carried into the super 
imposed courses, and can only be rectified by using a greater or 
less quantity of mortar in one part or another, a course which 
is injurious to the work. 

A common but improper method of building thick brick walls 
is to lay up the outer stretcher-courses between the header- courses, 
and then to throw mortar into the trough thus formed, making 
it semi-fluid by the addition of a large dose of water, then throw- 
ing in the brick (bats, sand, and rubbish are often substituted for 
bricks), allowing them to find their own bearing ; when the 



256 MASONRY. — BRICK MASONRY. 

trough is filled it is plastered over with stiff mortar and the 
header-course laid and the operation repeated. This practice 
may have some advantage in celerity in executing work, but 
none in strength or security. 

Amount of Moktar keqijired. — The thickness of the mortar- 
joints should be about :^ to f of an inch. Thicker joints are very 
common, but should be avoided. If the bricks are even fairly 
good the mortar is the weaker part of the wall ; hence the less 
mortar the better. Besides, a thin layer of mortar is stronger 
under compression than a thick one. The joints should be as 
thin as is consistent with their insuring a uniform bearing and 
allowing rapid work in spreading the mortar. The joints of out- 
side walls should be thin in order to decrease the disintegration 
by weathering. The joints of inside walls are usually made from 
f to ^ inch thick. 

The proportion of mortar to brick will vary with the size of the 
brick and with the thickness of the joint. With the standard brick 
(8J X 4 X ^i inches) the amount of mortar required will be as 
follows : 

Mortar required. 
Thickness of Joints. 

Per Cubic Yard. Per 1000 Brick. 

Cubic Yards. Cubic Yards. 

i to finch 0.30 to 0.40 0.80 to 0.90 

1"! " 0.20 " 0.30 0.40 *♦ 0.60 

i '' 0.10 '' 0.15 0.15 "0.20 

Face- or Pressed-brick Work. — This term is applied to 
the facing of walls with better bricks and thinner joints than the 
backing. 

The bricks are pressed, of various colors, and are laid in colored 
mortar. The bricks ^re laid in close joint, usually J inch thick, 
and set with an imperceptible batter in themselves, which may 
not be seen when looking at the work direct, but makes the 
joint a prominent feature and gives the work a good appearance. 
The brick of each course must be gauged with care and exactness, 
so that the joints may appear all alike. The bond used for the 
face of the wall is called the '* running bond," the bricks are 
clipped on the back, and a binder placed transversely therein to 
bond the facing to the backing. ' The joints in the backing being 
thicker than those of the face- work, it is only in every six or 
seven courses that they come to the same level, so as to permit 
headers being put in. This class of work requires careful watch- 



BRICK MASONRY IMPERVIOUS TO WATER. 2J.7 

iug to see that the binders or headers are put in; it frequently 
happens that the face-work is hiid up without having any bond 
with the backing. 

In white- joint work the mortar is composed of white sand and 
fine lime putty. The mason when using this mortar spreads it care 
fully on the bed of the brick which is to be laid in such a way 
that when the brick is set the mortar will protrude about half an 
inch from the face of the wall. When there are a number laid, 
and before the mortar becomes too hard, the mortar that pro 
trudes is cut off flush with the wall, the joint struck downwards, 
and the upper and lower edges cut with a knife guided by a small 
straight-eage. When the front is built the whole is cleaned 
down with a solution of muriatic acid and water, not too strong, 
and sometimes oiled with linseed-oil cut with turpentine and ap- 
plied with a flat brush. After the front is thoroughly cleaned 
with the muriatic acid solution it should be washed with clean 
water to remove all remains of the acid. 

When colored mortars are required the lime and sand should 
be mixed at least 10 days before the colored pigments nre added 
to it, and they should be well soaked in water before being added 
to the mortar. 

Brick Masonry Impervious to Water. 

It sometimes becomes necessary to prevent the percolation of 
water through brick walls. A cheap and effective process has 
not yet been discovered and many expensive trials have proved fail 
ures. Laying the bricks in asphaltic mortar and coating the walls 
with asphalt or coal-tar are successful. "Sylvester's Process for 
Repelling Moisture from External Walls " has proved entirely 
successful. The process consists in using two w^ashes for covering 
the surface of the walls, one composed of Castile soap and water, 
and one of alum and water. These solutions are applied alter- 
nately until the wails are made impervious to water. 

Efflorescence. 

Masonry, particularly in moist climates or damp places, is fre- 
quently disfigured by the formation of a white efflorescence on the 
surface. This deposit generally originates with the mortar. The 
water which is absorbed by the mortar dissolves the salts of soda, 
potash, magnesia, etc., contained in the lime or cement, and on 
(evaporating deposits thc^e sails as a whitt; ( fn()ie>C( nee on the 
surface. With lime mortar the deposit is fn qiuntly very heavy, 
and. usually, it is heavier with Roscndale than with Port hind 
cement. The efflorescence soinelinies orginates in the brick, 



258 MASOXRY. — REPAIR OF MASOXRY. 

particularly if the brick was burned with sulphurous coal 
or was made from clay containing iron pyrites ; and when the 
brick gets wet the water dissolves the sulphates of lime and mag- 
nesia, and on evaporating leaves the crystals of these salts on the 
surface. The crystallization of these salts withm the pores of the 
mortar and of the brick or stone causes disintegration, and acts 
in many respects like frost. 

The efflorescence may be entirely prevented by applying ** Syl- 
vester's " washes, composed of the same ingredients and applied 
in the same manner as for rendering masonry impervious to 
moisture. It can be much diminished by using impervious mortar 
for the face of the joints. 

Repair of Masonry, 

In effecting repairs in masonry, when new work is to be con- 
nected with old, the mortar of the old must be thoroughly cleaned 
off along the surface where the junction is to be made and the 
surface thoroughly wet. The bond and other arrangements will 
depend upon the circumstances of the case. The surfaces con- 
nected should be fitted as accurately as practicable, so that by 
using but little mortar no disunion may take place from settling. 

As a rule, it is better that new work should butt against the old, 
either with a straight joint visible on the face, or let into a chase, 
sometimes called a ' slip- joint," so that the straight joint may not 
show ; but if it is necessary to bond tiiem together the new work 
should be built in a quick-setting cement mortar and each part 
of it allowed to set before being loaded. 

In pointing old masonry all the decayed mortar must be com- 
pletely raked out with a hooked iron point and the surfaces well 
wetted before the fresh mortar is applied. 

Definitions of the Terms used in Masonry. 

Abutment : 1. That portion of the masonry of a bridge or dam 
upon which the ends rest, and which connects the superstructure 
with the adjacent banks. 2. A structure that receives the lateral 
thrust of an arch. 

Arris : The external angle or edge formed by the meeting of 
two plane or curved surfaces, whether walls or the sides of a 
slick or sloiic. 

Backed : Built on the rear face. 

Backing : The rough masonry of a wall faced with cut stone. 



DEFIKITIOKS OF THE TEKMS USED IK MASONHY. 259 

Batter : The slope or incliiuition given to the face of a wall. 
It is expressed by dividing the height by the horizontal distance. 
It is described by stating the extent of the deviation from the 
vertical, as one in twelve, or one inch to the foot. 

Bats : Broken bricks. 

Bearing-blocks or Templets : Small blocks of stone built in 
the wall to support the ends of particular beams. 

Belt-stones or -courses : Horizontal bauds or zones of stone 
encircling a building or extending through a wall. 

Blocking-course : A course of stones placed on the top of a 
cornice, crowning the walls. 

Bond. — The disposing of the blocks of stone or bricks in the 
wall so as to form the whole into a firm structure by a judicious 
overlapping of each other so as to break joint. 

A stone or brick which is laid with its length across the wall, 
or extends through the facing-course into that behind, so as to 
bind the facing to the backing, is called a ** header" or **bond." 

Bonds are described by various names, as : 

Binders^ when they extend only a part of the distance across 
the wall. 

Through-bonds y when they extend clear across from face to 
back. 

Heart-hondy when two headers meet in the middle of the wall 
and the joint between them is covered by another header. 

Perpend-bond signifies that a header extends through the whole 
thickness of the wall. 

Chain-bond is the building into the masonry of an iron bar, 
chain, or heavy timber. 

Gross-bond : A bond in which the joints of the second stretcher- 
course come in the middle of the first ; a course composed of 
headers and stretchers intervening. 

Block- and cross-bond : The face of the wall is put up in cross- 
bond and the backing in block-bond. 

EnglisJi bond (brick masonry) consists of alternate courses of 
headers and stretchers. 

Flemish-bond (brick masonry) consists of alternate headers and 
stretchers in the same course. 

Blind bond is used to tie the front couise to the wall in pressed- 
brick work where it is not desirable that any headers should be 
seen in the face-work. 

To form this bond the face brick is trimmed or clipped off at 
both ends, so that it will admit a binder to set in transversely 
from the face of tlie wall, and QVQvy laj'cr of these bind rs should 



2C0 DEFIJ^ITIONS OF THE TERMS USED IX MASOKRY. 

be tied with a heiider-course tlie whole length of the wnll. The 
binders should be put in every fifth course, and the backing 
should be done in a most substantial naanner, with hard brick 
laid in close joint, for the reason that the face-work is laid in a 
fine putty mortar, and the joints consequently close and tight; 
and if the backing is not the same the pressure upon the wall 
will make it settle and draw the wall inward. 

The common form of bond in brickwork is to lay three or five 
courses as stretchers; then a header- course. 

Bond-stones in Piers. — *' Every pier built of brick, contain- 
ing Jess than nine superficial feet at the base, supporting any 
beam, girder, arch, or column on which a wall rests, or lintel 
spanning an opening over ten feet and supporting a wall, shall 
at intervals of not over thirty inches apart in height have built 
into it a bond-stone not less than four inches thick, or a cast-iron 
plate of sufficient strength, and the full size of the piers/' (N. Y. 
Building Laws, 1896.) 

Breast- WALL • One built to prevent the falling of a vertical 
face cut into the natural soil; in distinction to a retaining wall, etc. 

Brick Ashlar : Walls with ashlar facing backed with bricks. 

Build or Rise : That dimension of the stone which is perpen- 
' dicular to the quarry-bed. 

Buttress A vertical projecting piece of stone or brick 
masonry built in front of a wall to strengthen it. 

Closers are pieces of brick or stone inserted in alternate 
courses of brick and broken ashlar masonry to obtain a bond. 

Cleaning Down consists in washing and scrubbing the stone- 
work with muriatic acid and water. Wire brushes are generally 
used for marble and sometimes for sandstone. Stiff bristle 
brushes are ordinarily used. The stones should be scrubbed 
until all mortar-stains and dirt are entirely removed. 

For cleaning old stonework the sand-blast operated either by 
steam or compressed air is used. Brick masonry is cleaned in 
the same manner as stone masonry. During the process of clean- 
ing all open joints under window-sills and elsewhere should be 
pointed. 

Coping. — The coping of a wall consists of large and heavy 
stones, slightly projecting over it at both sides, accurately bedded 
on the wall, and jointed to each other with cement mortar. Its 
use is to shelter the mortar in the interior of the wall from the 
woa^her, and to protect b}' its weight the s'^^aller Ptnre« below it 
Irotn b ing knocked off or picked out. ('oping stones should be 
no sh:iped that water may rapidly run off" from them. 



BEFIKTTIOKS 01^ THE TERMS tTSElD IK MASOHRY. 2(51 

For coping-stones the objections with regard to excess of 
length do not apply; this excess may, on the contrary, prove fa- 
vorable, because, the number of top joints being thus diminished, 
the mass beneath the coping will be better protected. 

Additional stability is given to a coping by so connecting the 
coping-stones together that it is impossible to lift one of them 
without at the same time lifting the ends of the two next it. 
This is done either by means of iron cramps inserted into holes 
in the stones and fixed there with lead, or, better still, by means 
of dowels of wrought iron, cast iron, copper, or hard stone. The 
metal dowels are inferior in durability to those of hard stone, 
though superior in strength. Copper is strong and durable, but 
expensive. The stone dowels are small prismatic or cylindrical 
blocks, each of which fits into a pnir of opposite holes in the con- 
tiguous ends of a pair of coping-stones and fixed with cement 
mortar. 

The under edge should be throated or dripped, that is, grooved, 
so that the drip will not run back on the wall, but drop from the 
edge. 

Coping is divided into three kinds \ 

Parallel coping, level on top. Feather -edged coping, bedded 
level and sloping on top. Saddle-hack coping has a curved or 
doubly inclined top. 

Corbel : A horizontal projecting piece or course of masonry 
which assists in supporting one resting upon it which projects 
still further. 

Cornice : The ornamental projection at the eaves of a build- 
ing or at the top of a pier or any other structure. 

Counterfort : Vertical projections of stone or brick masonry 
built at intervals along the hack of a wall to strengthen it, and 
generally of very little use. 

Course. — The term course is applied to each horizontal row or 
layer of stones or bricks in a wall; some of the courses have par- 
ticular names, as : 

Plintli'CouTse, a lower, projecting, square-faced course; also 
called the water -tahle. 

Blocking -couvs^, laid on top of the cornice. 

Bonding -course, one in which the stones or bricks lie with tbeir 
length across the wall; also called heading course. 

Stretching -course, consisting of stretchers. 

Sp ringing-course, the course fr^m which an arch springs. 

String cours'.\ ji projecting couise. 

liowlock-couise, bricks set on ed^e. 



262 DEFINITIONS OF THE TERMS USED IK MASOKRY. 

Cramps Bars of iron having the ends turned at right angles 
to the body of the bar, and inserted in holes and trenches cut in 
the upper sides of adjacent stones to hold them together (see un- 
der Coping). 

CuTWATEB OR STARLING : The projecting ends of a bridge- 
pier, etc., usually so shaped as to allow water, ice, etc, to strike 
them with but little injury. 

Dowels. — Straight bars of iron, copper, or stone which are 
pLiced in holes cut in the upper bed of one stone and in the lower 
bed of the next stone above. They are also placed horizontally 
in the adjacent ends of coping-stones (see under Coping). 
Cramps and dowels are fastened in place by pouring melted lead, 
sulphur, or cement grout around them. 

Dry Stone Walls may be of any of the classes of masonry 
previously described, with the single exception that the mortar 
is omitted. They should be built according to the principles laid 
down for the class to which they belong. 

Face : The front surface of the wall. 

Facing : The stone which forms the face or outside of the wall 
exposed to view. 

Footing : The projecting courses at the base of a wall for the 
purpose of distributing the weight over an increased area, and 
thereby diminishing the liability to vertical settlement from com- 
pression of the ground. 

Footings, to have any useful effect, must be secnrely bonded 
into the body of the work, and have sufficient strength to resist 
the cross-strains to which they are exposed. 

The beds should be dressed true and parallel. 

Too much care cannot be bestowed upon the footing-courses 
of any building, as upon them depends much of the stability of 
the work. If the bottom course be not solidly bedded, if any 
rents or vacuities are left in the beds of the masonry, or if the 
materials be unsound or badly put together, the effects of such 
carelessness will show themselves sooner or later, and afwaysata 
period when remedial efforts are useless. 

Footing-courses.— (N. Y. Building Laws, 1899) : '* The foot- 
ing- or base-course shall be of stone or concrete, or both, or of 
concrete and stepped-up brickwork, of sufficient thickness and 
area to safely bear the weight to be imposed thereon. If the 
footing- or base-course be of concrete, the concrete shall not be 
less than 12 inches thick ; if of stones Iho stones shall not be less 
than 2 by 3 feet, and at least 8 iiiclies in thickness for walls, and 



DEFINITIONS OF THE TERMS USED IN' MASONRY. SG3 

at Last 12 inches wider than the bottom width of caid wal's, and 
not less than 10 inches in thickness if under piers, columns, or 
postJ. Ail base-stones shall be well bedded and laid crosswise, 
edge to edge." 

Sec. 24. Pressure under Footings of Foundations.— The 
loads exerting pressure under the footings of foundations in build- 
ings more than three (3) stories in height are to be computed as 
follows : For warehouses and factories they are to be made the 
full dead load and the full live load established by Section 130 of 
this Code. In stores and buildings for light manufacturing 
purposes they are to be the full dead load and 75 per cent of the 
live load established by Section 130 of this Code. 

In churches, school-houses and places of public amusement or 
assembly, they are to be the full dead load and 75 per cent of 
the live load established by Section 130 of this Code. 

In office buildings, hotels, dwellings, apartment houses, tene- 
ment houses, lodging houses, and stables they are to be the full 
dead load and 60 per cent of the live load established by Section 
130 of this Code. 

Footings shall be so designed that the loads will be as nearly 
uniform as possible and not in excess of the safe bearing capacity 
of the soil, as established by Section 23 of this Code. 
• If, in place of a continuous foundation-wall, isolated piers 
are to be built to support the superstructure, where the nature of 
the ground and the character of the building make it necessary, 
inverted arches resting on a proper bed of concrete, both de- 
signed to transmit with safety the superimposed loads, shall be 
turned between the piers. The thrust of the outer piers shall be 
taken up by suitstble wrought iron or steel rods and plates. 

Grillage beams of wrought iron or steel resting on a proper 
concrete bed may be used. Such beams must be provided with 
separators and bolts enclosed and filled solid between with con- 
crete and of such sizes and so arranged as to transmit with 
safety the superimposed loads. 

*• If stepped-up footings of brick are used in place of stone above 
the concrete the steps or offsets, if laid in single courses, shall 
each not exceed 1^ inches, or, if laid in double courses, then each 
shall not exceed three inches, starting with the brickwork covering 
the entire width of the concrete." 

Chicago Building Ordinances, 1893 : " The offsets of founda- 
tions of concrete alone shall not exceed one-half the height of tlie 
respective courses. If reinforced by rails or beams the offsets 



2G4 DEFINITIONS OF THE TERMS USED IK" MASOKHY. 

must be so adjusted that the fibie-strain per square inch shall not 
exceed 12,000 pounds for iron or 16,000 pounds for steel. 

•*The offsets in layers of dimension stone must not be more 
than three quarters of the height of the individual stones. 

" In brick piers there shall be at every offset a bond-stone at 
least 8 in. thick, and at the top of each pier a cap-stone at least 
10 in. thick, or in all such cases a bond-plate of cast or rolled 
iron." 

Gauged-work : Bricks cut and rubbed to the exact shape re- 
quired. 

Grout is a thin or fluid mortar made in the proportion of 1 
of cement to 1 or 2 of sand. 

It is used to fill up the voids in v^alls of rubble masonry and 
brick. Sometimes the interior of a wall is built up dry and grout 
poured in to fill the voids. Unless specifically instructed to per- 
mit its use, grout should not be used unless in the presence of the 
inspector. When used by masons without instructions it is usu- 
ally for the purpose of concealing bad work. 

Grout is used for solidifying quicksand. A series of pipes are 
sunk into the layer of quicksand, and through each alternate one 
cement grout is forced under pressure. This, seeking an outlet 
by the line of least resistance, will make an exit by the adjoining 
pipe, which opens into the air above ; but in so doing the pressure- 
valve at the bottom of the pipe is opened and results in a dif- 
fusing of the grout in the surrounding quicksand, which forms 
with it an artificial stone, and by gradually raising the pipes a 
wall of stone is formed in the layer of quicksand. 

The term grout is also applied to the waste stone in quarries. 

Grouting is pouring fluid mortar over last ctourse for the pur- 
pose of filling all vacuities. 

Header. — Also called a bond. A stone or brick whose greatest 
dimension lies perpendicular to the face of the wall, and used for 
the purpose of tying the face to the backing (see Bond). A trick 
of masons is to use '* blind headers," or short stones that look like 
headers on the face, but do not go deeper into the wall than the 
adjacent stretchers. When a course has been put on top of these 
they are completely covered up, and, if not suspected, the fraud 
will never be discovered unless the weakness of the wall reveals it. 

In facing brick walls with pressed brick the bricklayer will 
frequently cut the headers for the purpose of economizing the 
more expensive material ; thus great watchfulness is necessary to 
secure a good bond between the facing and common brick. 



DEFTNITIOKS OF THE TERMS USED IK MASONRY. 2G5 

Headers. — N. Y. Building Laws, 1899 : "All stone foundation- 
walls 24 inches or less in thickness shall have at least one header 
extending through the wall in every 3 feet in height from 
the bottom of the wall, and in every 3 feet in length, and if 
over 24 inches in thickness shall have one header for every 6 
superficial feet on both sides of the wall, and running into the 
wall at least 2 feet. All headers shall be at least 12 inches in 
width and 8 inches in thickness, and consist of good, flat stone. 

*' In all brick walls every sixth course shall be a heading- 
course, except where walls are faced with brick in running bond, 
in which latter case every sixth course shall be bonded into the 
backing by cutting the course of the face-brick and putting in 
diagonal headers behind the same, or by splitting the face-brick 
in half and backing the same with a continuous row of headers." 

Joints. — The mortar layers between the stones or bricks are 
called the joints. The horizontal joints are called " bed-joints" ; 
the end-joints are called the vertical joints, or simply the 
*' joints." 

Excessively thick joints should be avoided. In good brick- 
work they should be about J to | inch thick ; for ashlar ma- 
sonry and pressed-brick work about J to ^ inch thick ; for rubble 
masonry they vary according to the character of the work. 

The joints of both stone and brick masonry are finished in 
different ways, with the object of presenting a neat appearance 
and of throwing the rain-water away from the joint. 

Flush Joints. — In these the mortar is pressed flat with the 
trowel and the surface of the joint is flush with the face of the 
wall. 

Struck-joints are formed jj pressing or striking back with 
the trowel the upper portion of the joint while the mortar is 
moist, so as to form an outward sloping surface from the bottom 
of the upper course to the top of the lower course. This joint is 
also designated by the name '* weather-joint." Masons generally 
form this joint so that it slopes inwards, thus leaving the upper 
arris of the lower course bare and exposed to the action of the 
weather. The reason for forming it in this improper manner 
is that it is easier to perform. 

Keyed Joints are formed by drawing a curved iron key or 
jointer along the centre of the flushed joint, pressing it hard, so 
that the mortar is driven in beyond the face of the wall , a groove 
of curved section is thus formed, having its surface hardened by 
the pressure. 



266 i)EFi2sriTio:tirs of the terms used in masonry. 

White-skate or Groove Joint is employed in frout brick- work. 
Il is {iboiit y\ iuch thick. It is formed with u joiuter having 
the width of the intended joint. It is uuided iiloug tbe joint b}'' 
a straight-edge and leaves its impress upon the material. 

Joggle : A joint-piece or dowel pin let into adj iceut faces of 
two stones to hold them in position. It may vary in form, and 
approach in its shape either the dowel or clamp. 

Jamb: The sides of an opening left in a wall. 

Lintel : The stone, wood, or iron beam used to cover a nar- 
row opening in a wall. 

One-man Stone : A stone of such size as to be readily lifted 
by one man. 

Parapet Wall is a low wall running along the edge of a ter- 
race or roof to prevent people from falling over. 

Pointing a piece of masonry consists in scraping out the mor- 
tar in which the siones were laid from the face of the joints for a 
depth of from ^ to 2 inches, and filling the groove so made with 
clear Portland-cement mortar or with mortar made of 1 part of 
cement and 1 part of sand. 

The object of pointing is that ihe exposed edges of the joints 
are always deficient in density and hardness, and the mortar near 
the surface of the joint is specially subject to dislodgment, since 
the contraction and expansion of the masonry are liable either to 
separate the stone from the mortar or to crack the mortar in the 
joint, thus permitting the entrance of rain-water, which freezing 
forces the mortar from the joints. 

The pointing-mortar, when ready for use, should be rather in- 
coherent and quite deficient in plasticity. 

Before applying the pointing the joint must be well cleansed 
by scraping and brushing out the loose matter, then thoroughly 
saturated with water, and maintained in such a condition of 
dampness that the stones will neither absorb water from the mor- 
tar nor impart any to it. Walls should not be allowed to dry too 
rapidly after pointing. 

Pointing should not be prosecuted either during freezing or 
excessively hot weather. 

The pointing-mortar is applied with a mason's trowel, and the 
joint well calked with a calking-iron and hammer. In the very 
best work the surface of the mortar is rubbed smooth with a steel 
polisbing-tool. The form given to the finished joint is the same 
as described under Joints. 

Pointing with colored mortar is frequently employed to im- 



DEFINITIONS OF THE TERMS USED IN MASONRY. 267 

prove the appearance of the work. Various colors are used, as 
white, black, red, brown, etc., dilfereut-colored pigments being 
added to the mortar to produce the required color. 

Tuck-pointing, used chiefly for brickwork, consists of a project- 
ing ridge with the edges neatly pared to an uniform breadth of 
about \ inch. White mortar is usually employed for this class of 
pointing. 

Mauy authorities consider that pointing is not advisable for 
new work, as the joints so formed are not as enduring as those 
which are finished at the time the masonry is built. Pointing is, 
moreover, often resorted to when it is intended to give the work 
a superior appearance, and also to conceal defects in inferior 
work. 

Pallets, Plugs : Wooden bricks inserted in walls for fastening 
trim, etc. 

Plinth : A projecting base to a wall ; also called '* water- 
table. '^ 

Quarry-faced or Kock-faced Masonry : That in which the 
face of the stone is left untouched as it comes from the quarry. 

Pitched-face Masonry : That in which the face of the stone 
is roughly dressed with the pitching-chisel so as to give edges 
that are approximately true. 

Quoin : A corner-stone. A quoin is a header for one face 
and a stretcher for the other. 

Rip-rap. — Rip-rap is composed of rough undressed stone as it 
comes from the quarry, laid dry about the base of piers, abut- 
ments, slopes of embankments, etc., to prevent scour and w^ash. 
When used for the protection of piers the stones are dumped in 
promiscuously, their size depending upon the material and the 
velocity of the current. Stones of 15 to 25 cubic feet are fre~ 
quently employed. When used for the protection of banks the 
stones are laid by hand to a uuiform thickness. 

Rise : That dimension of a stone which is perpendicular to its 
quarry- bed (see Build). 

Retaining Wall or Revetment : A wall built to retain earth 
deposited behind it (see Breast-wall). 

Reveal : The exposed portion of the sides of openings in walls 
in front of the recesses for doors, window-frames, etc. 

Slope- WALL Masonry : A slope-wall is a thin layer of masonry 
used to protect the slopes of embankments, excavations, canals, 
river-banks, etc., from rain, waves, weather, etc. 

Slips : See Wood Bricks. 



268 DEFI]SriTI0]!5'S of the terms used in MASOKE.Y. 

Spall. — A piece of stone chipped off by the stroke of a ham- 
mer. 

Sill. — The stooe, iron, or wood on which the window or door 
of a building rests. 

In setting stone sills the mason beds the ends only; the middle 
is pointed up after the building is enclosed. They should be set 
perfectly level lengthwise, and have an inclination crosswise, so 
the water may flow from the frame. 

Stone Paving consists of roughly squared or unsquared blocks 
of stone used for paving the waterway of culverts, etc., it is 
laid both dry and in mortar. 

Starling : See Cutwater. 

Stretcher : A stone or brick whose greatest dimension lies 
parallel to the face of the wall. 

String-course : A horizontal course of brick or stone masonry 
projecting a little beyond the face of the wall. Usually intro- 
duced for ornament. 

Templets : Bearing-blocks; small blocks of stone inserted in 
the wall to support the ends of particular beams. 

Two-men Stone : Stone of such size as to be conveniently 
lifted by two men. 

Toothing : Unfinished brickwork so arranged that every alter- 
nate brick projects half its length. 

Water-table : See Plinth. 

Wood Bricks, Pallets, Plugs, or Slips are pieces of wood 
laid in a wall in order the better to secure any woodwork that it 
may be necessary to fasten to it. Great injury is often done to 
walls by driving wood plugs into the joints, as the}^ are apt to 
shake the work. Hollow porous terra-cotta bricks are frequently 
used instead of wood, bricks, etc. 

Walls are constructions of stone, brick, or other materials, 
and serve to retain earth or water, or in buildings to support the 
roof and floors and to keep out the weather. The following 
points should be attended to in the constructio: . of walls : 

The whole of the walling of a building should be carried up 
simultaneously; no part should be allowed to rise more than 
about 3 feet above the rest; otherwise the portion first built will 
settle down to its bearings before the other is attached to it, and 
then the settlement which takes place in the newer portion will 
cause a rupture, and cracks will appear in the structure. If it 
should be necessary to carry up one part of a wall before the 
other, the end of that portion first built should be racked hnck, 



DEFINITIOI^S OF THE TERMS USED IK MASONRY. 269 

that is, left in steps, each course projecting farther than the one 
above it. 

Work should not be hurried along unless done in cement mor- 
tar, but given time to settle to its bearings. 

Walls, Piers, and Partitions. ^ 

(N. Y. Building Code, 1899.) 

Sec. 27. Materials of Walls.— The walls of all buildings, 
other than frame or wood buildings, shall be constructed of stone, 
brick, Portland cement concrete, iron or steel or other hard, in- 
combustible material, and the several component parts of such 
buildings shall be as herein provided. All buildings shall be en- 
closed on all sides with independent or party walls. 

Sec. 28. Walls and Piers. — In all walls of the thickness 
specified in this code, the same amount of materials may be used 
in piers or buttresses. Bearing walls shall be taken to mean those 
walls on which the beams, girders, or trusses rest. - If any hori- 
zontal section through any part of any bearing wall in any build- 
ing shows more than 30 per centum area of flues and open- 
ings, the said wall shall be increased 4 inches in thickness for 
every 15 per centum or fraction thereof of flue or opening 
area in excess of 30 per centum. 

The walls and piers of all buildings shall be properly and 
solidly bonded together with close joints filled with mortar. 
They shall be built to a line and be carried up plumb and 
straight. The walls of each story shall be built up the full 
thickness to the top of the beam above. All brick laid in non- 
freezing weather shall be wet before being laid. Walls or piers, 
or parts of walls or piers, shall not be built in freezing weather, 
and if frozen, shall not be built upon. 

All piers shall be built of stone or good, hard, well- burnt brick 
and laid in cement mortar. Every pier built of brick, containing 
less than 9 superficial feet at the base, supporting any beam, 
girder, arch, or column on which a wall rests, or lintel spanning 
an opening over 10 feet and supporting a wall, shall at intervals 
of not over 30 inches apart in height have built into it a bond 
stone not less than 4 inches thick, or a cast-iron plate of suffi- 
cient strength, and the full size of the piers. For piers fronting 
on a street the bond stones may conform with the kind of stone 
used for the trimmings of the front. Cap stones of cut granite 



370 DSFIIS-ITIONS OF THE TERMS USED lis" MASOI^RY. 

or blue stono, proportioned to the weight to be carried, but not 
less than 5 inches in thickness, by the full size of the pier, or 
cast-iron plates of equal strength by the full size of the pier, shall 
be set under all columns or girders except where a 4 inch 
bound stone is placed immediately below said cap stone, in 
which case the cap may be reduced in horizontal dimensions at 
the discretion of the Commissioner of Buildings having jurisdic- 
tion. Isolated brick piers shall not exceed in height ten times 
their least dimensions. Stone posts for the support of posts or 
columns above shall not be used in the interior of any building. 
Where walls or piers are buih of coursed stones, with dressed 
level beds and vertical joints, the Department of Buildings shall 
have the right to allow such walls or piers to be built of a less 
thickness than specified for brickwork, but in no case shall said 
walls or piers be less than three quarters of the thickness pro- 
vided for brickwork. 

In all brick walls every sixth course shall be a heading course, 
except where walls are faced with brick in running bond, in 
which latter case every sixth course shall be bonded into the 
backing by cutting the course of the face brick and putting in 
diagonal headers behind the same, or by splitting the face brick 
in balf and backing the same with a continuous row of headers. 
Where face brick is used of a different thickness from the brick 
used for the backing, the courses of the exterior and interior 
brickwork shall be brought to a level bed at intervals of not 
more than ten courses in height of the face brick, and the face 
brick shall be properly tied to the backing by a heading course 
of the face brick. All bearing walls faced with brick laid in 
running bond shall be 4 inches thicker than the walls are 
required to be under any section of this code. 

Sec. 29. Ashlaii. — Stone used for the facing'of any building, 
and known as ashlar, shall be not less than 4 inches thick. 

Stone ashlar shall be anchored to the backing and the backing 
shall be of such thickness as to make the walls, independent of 
the ashlar, conform as to the thickness with the requirements 
of sections 31 and 32 of this Code, unless the ashlar be at least 8 
inches thick and bonded into the backing, and then it may be 
counted as part of the thickness of the wall. 

Iron ashlar plates used in imitation of stone ashlar on the face 
of a wall shall be backed up with the same thickness of brick- 
work as stone ashlar. 



DEFINITIONS OF THE TERMS USED IN MASONRY. 27 L 

Sec. 30. Mortar for Walls and Ashlar. — All foundation 
walls, isolated piers, parapet walls, and chimney above roofs 
shall be laid in cement mortar, but this shall not prohibit the use 
in cold weather of a small proportion of lime to prevent the mortar 
from freezing. All other walls built of brick or stone shall be 
laid in lime, cement or lime and cement mortar mixed. 

The backing-up of all stone ashlar shall be laid up with cement 
mortar, or cement and lime mortar mixed, but the back of the 
ashlar may be parged with lime mortar to prevent discolorations 
of the stone. 

Sec. 31. Walls for Dwelling Houses. — The expression 
** walls for dwelling houses " shall be taken to mean [and include 
in this class walls for the following buildings: 

Dwellings, asylums, apartment-houses, convents, club-houses, 
dormitories, hospitals, hotels, lodging-houses, tenements, parish 
buildings, schools, laboratories, studios. 

The walls above the basement of dwelling-houses not over 
three stories and basement in height, nor more than 40 feet in 
height, and not over 20 feet in width, and not over 55 feet in 
depth, shall have side and. party walls not less than 8 inches 
thick, and front and rear walls not less than 12 inches thick. All 
walls of dwellings exceeding 20 feet in width, and not exceeding 
40 feet in height, shall be not less than 12 inches thick. All 
walls of dwellings 26 feet or less in width between bearing walls 
which are hereafter erected or which may be altered to be used 
for dwellings, and being over 40 feet in height and not over 50 
feet in height, shall be not less than 12 inches thick above the 
foundation wall. No wall shall be built having a 12-inch thick 
portion measuring vertically more than 50 feet. If over 50 feet 
in height, and not over 60 feet in height, the wall shall be not 
less than 16 inches thick in the story next above the foundation 
walls and from thence not less than 12 inches to the top. If 
over 60 feet in height, and not over 75 feet in height, the walls 
shall be not less than 16 inches thick above the foundation walls 
to the height of 25 feet, or to the nearest tier of beams to that 
height, and from thence not less than 12 inches thick to the top. 
If over 75 feet in height, and not over 100 feet in height, the 
walls shall be not less than 20 inches thick above the foundation 
walls to the height of 40 feet, or to the nearest tier of beams to 
that height, thence not less than 16 inches thick to the height of 
75 feet or to the nearest tier of beams to that height, and thence 
not less than 12 inches thick to the top. If over 100 feet in 



272 DEFIXITI0X5 OF THE TERMS USED IX MASOXRT. 

lieiglit, and not over 125 feet in height, the walls shall be not less 
tlian 24 inches thick above the foundation walls to the height of 
40 feet, or to the nearest tier of beams to that height, thence not 
less than 20 inches thick to the height of 75 feet, or to the near- 
est tier of beams to that height, thence not less than 16 inches 
thick to the height of 110 feet, or to the nearest tier of beams to 
that height, and thence not less than 12 inches thick to the top. 
If over 125 feet in height, and not over 150 feet in height, the 
walls shall be not less than 28 inches thick above the foundation 
walls to the height of 30 feet, or to the nearest tier of beams to 
that height; thence not less than 24 inches thick to the height of 
65 feet, or to the nearest tier of beams to that height; thence not 
less than 20 inches thick to the height of 100 feet, or to the near- 
est tier of beams to that height; thence not less than 16 inches 
thick to the height of 135 feet, or to the. nearest tier of beams to 
that height, and thence not less than 12 inches thick to the top. 
If over 150 feet in height, each additional 30 feet in height or part 
thereof next above the foundation walls shall be increased 4 
inches in ihickness, the upper 150 feet of wall remaining the same 
as specified for a wall of that height. 

All non-fireproof dwelling-houses erected under this section 
exceeding 26 fett in width shall have brick fore and aft partition 
walls. All non-bearing walls of buildings hereinbefore in this sec- 
tion specified may be 4 inches less in thickness, provided, however, 
that none are less than 12 inches thick, except as in this code speci- 
fied. Eight-inch brick partition walls mavbe built to support the 
beams in such buildings in which the distance between the main 
or bearing walls is not over 33 feet ; if the distance between the 
main or bearing walls is over 33 feet the brick partition wall 
shall be not less than 12 inches thick, provided that no clear span 
is over 26 feet. No wall shall be built having any one thickness 
measuring vertically more than 50 feet. This section shall not 
be construed to prevent the use of iron or steel girders, or iron or 
steel girders and columns, or piers of masonry for the support of the 
walls and ceilings over any room which has a clear span of more 
than 26 feet between walls, in such dwellings as are not con- 
structed fireproof, nor to prohibit the use of iron or steel girders, 
or iron or steel girders and columns in place of brick walls in 
buildings which are to be used for dwellings when constructed 
fireproof. If the clear span is to be over 26 feet, then the bearing 
walls shall be increased 4 inches in thickness for every 12|^ feet 
or part thereof that said span is over 26 feet, or shall have 



BEFlKIxrONS OF TTTI<: TEKMS USED IK MASOKKY. 2T2rt 

instead of tlie increased thickness sucli piers or buttresses as, in 
the judgment of the Commissioner of Buildings having jurisdic- 
tion, may be necessary. 

Whenever two or more dwelling-houses shall be constructed 
not over 12 feet 6 inches in width, and no"^ over 50 feet in height^ 
the alternating centre wall between any two such houses shall be 
of brick not less than 8 inches thick above the foundation wall ; 
and the ends of the floor-beams shall be so separated that 4 inches 
of brickwork will be between the beams where they rest on the 
said centre wall. 

Sec. 32. Walls for Warehouses. — The expression '' walls 
for warehouses " shall be taken to mean and include in this class 
walls for the following buildings : 

Warehouses, stores, factories, mills, printing-houses, pumping- 
stations, refrigerating-houses, slaughter-houses, wheelwright 
shops, cooperage shops, breweries, light- and power-houses, sugar 
refineries, office buildings, stables, markets, railroad buildings, 
jails, police stations, court-houses, observatories, foundries, ma- 
chine shops, public assembly buildings, armories, churches, 
theatres, libraries, museums. The walls of all warehouses 25 
feet or less in width between walls or bearings shall be not less 
than 12 inches thick to the height of 40 feet above the foundation 
walls. If over 40 feet in height, and not over 60 feet in height, 
the walls shall be not less than 16 inches thick above the founda- 
tion walls to the height of 40 feet or to the nearest tier of beams 
to that height, and thence not less than 13 inches thick to the 
top. If over 60 feet in height, and not over 75 feet in height, the 
walls shall be not less than 20 inches thick above the foundation 
walls to the height of 25 feet or to the nearest tier of beams to 
that height, and thence not less than 16 inches thick to the top. 
If over 75 feet in height, and not 100 feet in height, the walls 
shall be not less than 24 inches thick above the foundation walls 
to the height of 40 feet or to the nearest tier of beams to the 
height, thence not less than 20 inches thick to the height of 75 
feet or to the nearest tier of beams to that height, and thence not 
less than 16 inches thick to the top. If over 100 feet in height, 
and not over 125 feet in height, the wall shall be not less than 28 
inches thick above the foundation walls to the height of 40 feet 
or to the nearest tier of beams to that height, thence not less than 
24 inches thick to the height of 75 feet or to the nearest tier of 
beams to that height, tlK^nce not less than 20 inches tliick to the 
height of 110 feet or to the nearest tier of beams to lliiit heiglit, 



272i DEFIKITIOKS OP THE TERMS USED IN" MASONRY. 

and tlience not less than 16 inches thick to the top. If over 125 
feet in height, and not over 150 feet, the walls shall be not less 
than 32 inches thick above the foundation walls to the height of 
30 feet or to the nearest tier of beams to that height, thence not less 
than 28 inches thick to the height of 65 feet or to the nearest tier of 
beams to that height, thence not less than 24 inches thick to the 
height of 100 feet or to the nearest tier of beams to that height, 
thence not less than 20 inches thick to the height of 135 feet or to 
the nearest tier of beams to that height, and thence not less than 
16 inches thick to the top. If over 150 feet in height, each addi- 
tional 25 feet in height or part thereof next above the founda- 
tion walls shall be increased 4 inches in thickness, to the upper 
150 feet of wall remaining the same as specified for a wall of that 
height. 

If there is to be a clear span of over 25 feet between the bear- 
ing walls, such walls shall be 4 inches more in thickness than 
in this section specified, for every 12 J feet, or fraction thereof, 
that said walls are more than 25 feet apart, or shall have instead 
of the increased thickness such piers or buttresses as, in the judg- 
ment of the Commissioner of Buildings, may be necessary. 

The walls of buildings of a public character shall be not less 
than in this code specified for warehouses with such piers or such 
buttresses, or supplemental columns of iron or steel, as in the 
judgment of the Commissioner of Buildings having jurisdiction 
may be necessary to make a safe and substantial building. 

In all stores, warehouses, and factories over 25 feet in width 
between walls there shall be brick partition walls or girders 
supported on iron, steel, or wood columns, or piers of masonry. 

In all stores, warehouses, or factories, in case iron, steel, or wood 
girders, supported by iron, steel, or wood columns, or piers of 
masonry, are used in place of brick partition walls, the building 
may be 75 feet wide and 210 feet deep, when extending from street 
to street, or when otherwise located may cover an area of not 
more than 8000 superficial feet. When a building fronts on three 
streets it may be 105 feet wide and 210 feet deep, or if a corner 
building fronting on two streets.it may cover an area of not more 
than 12,500 superficial feet ; but in no case wider nor deeper, nor 
to cover a greater area, except in the case of fireproof buildings. 
An area greater than herein stated may, considering location and 
purpose, be allowed by the Board of Buildings when the proposed 
building does not exceed three stories in height. 

Sec. 33. Increased Thicknesses op Walls for Buildings 



\ BEFIlSriTlOKS OF THE TERMS USED IK MASON UY. 272e 

More tlian 105 Feet in Depth. — All buildings, not excepting- dwell- 
ings, that are over 105 feet in depth, without a cross- wjJl or 
proper piers or buttresses, shall have the side or bearing wal'.s 
increased in thickness four inches more than is specified in t:;e 
respective sections of this code for the thickness of walls for every 
105 feet, or part thereof, that the said buildings are over 105 feet 
in depth. 

Sec. 34. Reduced Thickness for Interior Walls. — In case the 
walls of any building are less than 25 feet apart, and less than 4.0 
feet in depth, or there are cross-walls which intersect the walls 
not more than 40 feet distant, or piers or buttresses built into the 
walls, the interior walls may be reduced in thickness in just pro- 
portion to the number of cross-walls, piers, or buttresses, and their 
nearness to each other ; provided, however, that this clause shall 
not apply to walls below 60 feet in height, and that no such wall 
shall be less than 12 inches thick at the top, and gradually in- 
creased in thickness by set-offs to the bottom. The Commissioner 
of Buildings having jurisdiction is hereby authorized and em- 
powered to decide (except where herein otherwise provided for) 
how much the walls herein mentioned may be permitted to be 
reduced in thickness, according to the peculiar circumstances of 
each case, without endangering the strength and safety of the 
building. 

Sec. 35. One story Brick Buildings.— One-story structures 
not exceeding a height of 15 feet may be built with 8- inch walls 
when the bearing walls are not more than 19 feet apart and the 
length of the 8-inch bearing walls does not exceed 55 feet. One- 
story and basement extensions may be built with 8-inch walls 
when not over 20 feet wide, 20 feet deep, and 20 feet high to 
dwellings. 

Sec. 36. Enclosure Walls for Skeleton Structures. — 
Walls of brick built in between iron or steel columns, and sup- 
ported wholly or in part on iron or steel girders, shall be not less 
than 12 inches thick for 75 feet of the uppermost height thereof, or 
to the nearest tier of beams to that measurement, in any building 
so constructed, and every lower section of 60 feet or to the nearest 
tier of beams to such vertical measurement, or part thereof, shall 
have a thickness of 4 inches more than is required for the sec- 
tion next above it down to the tier of beams nearest to the curb 
level; and thence downward, the thickness of walls shall in- 
crease in the ratio prescribed in Section 26, this Code. 

Sec. 37. Curtain Walls. — Curtnin wnlls built in between 



272(1 DEi'ixiTiOKS of the Terms used m masokry. 

piers or iron or steel coliiinns and not supported on steel or iron 
girders shall not be less than 12 inches thick, for 60 feet of the 
uppermost height thereof, or nearest tier of beams to that height, 
and increased 4 inches for every additional section of 60 feet or 
nearest tier of beams to that height. 

Sec. 38. Existing Pakty Walls.— Walls heretofore built for 
or used as party walls, whose thickness at the time of their erec- 
tion was in accordance with the requirements of the then exist- 
ing laws, but which are not in accordance with the requirements 
of this Code, may be used, if in good condition, for the ordinary 
uses of party walls, provided the height of the same be not in- 
creased. 

Sec. 39. Lining Existing Walls. — In case it is desired to 
increase the height of existing party or independent walls which 
are less in thickness than required under this Code, the same 
shall be done by a lining of brickwork to form a combined thick- 
ness with the old wall of not less than 4 inches more than the 
thickness required for a new wall corresponding with the total 
height of the wall when so increased in height. The said linings 
shall be supported on proper foundations and carried up to such 
height as the Commissioner of Buildings having jurisdiction may 
require. No lining shall be less than 8 inches in thickness, and 
all lining shall be laid up in cement mortar and thoroughly an- 
chored to the old brick walls wiih suitable wrought-iron anchors, 
placed 2 feet apart and properly fastened or driven into the 
old walls in rows alternating vertically and horizontally with 
each other, the old walls being first cleaned of plaster or other 
coatings where any lining is to be built against the same. No 
rubble wall shall be lined except after inspection and approval 
by the Department. 

Sec. 40. Walls of Unfinished Buildings. — Any. building 
the erection of which was commenced in accordance with specifi- 
cations and plans submitted to and approved by the Department 
of Buildings prior to the passage of this Code, if properly con- 
structed and in safe condition, may be completed, or built upon 
in accordance with the requirements of law, as to thickness of 
walls, in force at the time when such specification and plans 
were approved. 

Sec. 41. Walls Tied, Anchored, and Braced. — In no case 
shall any wall or walls of any building be carried up more than 
two stories in advance of any other wall, except by permission of 
the Commissioner of Buildings having jurisdiction, but this pro- 



DEPINITIOKS OF THE TERMS USED IK MASOKRY. 272^ 

liibition sliall not include the enclosure walls for skeleton build- 
ings. The front, rear, side, and party walls shall be properly 
bonded together, or anchored to each other every 6 feet in their 
height by wrought-iron tie-anchors not less than 1^ inches by 
f of an inch in size, and not less than 24 inches in length. The 
side anchors shall be built into the side or party walls not less 
than 16 inches, and into the front and rear walls, so as to secure 
the front and rear walls to the side, or party walls, when not 
built and bonded together. All exterior piers shall be anchored 
to the beams or girders on the level of each tier. The walls and 
beams of every building, during the erection or alteration thereof, 
shall be strongly braced from the beams of each story, and when 
required shall also be braced from the outside, until the building 
is enclosed. The roof tier of wood beams shall be safely anchored 
with plank or joist to the beams of the story below until the 
building is enclosed. 

Sec. 42. Arches and Lintels. — Openings for doors and win- 
dows in all buildings shall have good and sufficient arches of 
stone, brick, or terra-cotta, well built and keyed with good and 
sufficient abutments, or lintels of stone, iron, or steel of^ sufficient 
strength, which shall have a bearing at each end of not less than 
5 inches on the wall. On the inside of all openings in which 
lintels shall be less than the thickness of the wall to be supported, 
there shall be timber lintels, which shall rest at each end not 
more than 3 inches on any wall, which shall be chamfered at 
each end, and shall have a suitable arch turned over the timber 
lintel. Or the inside lintel may be of a cast iron, or wrought iron 
or steel, and in such case stone blocks or cast-iron plates shall not 
be required at the ends where the lintel rests on the walls, pro- 
vided the opening is not more than 6 feet in width. 

All masonry arches shall be capable of sustaining the weight 
and pressure which they are designed to carry, and the stress at 
any point shall not exceed the working stress for the material 
used, as given in section 139 of this Code. The rods shall be used 
where necessary to secure stability. 

Sec. 43. Parapet Walls. — All exterior and division or party 
walls over 15 feet high, excepting where such walls are to be 
finished with cornices, gutters, or crown mouldings, shall have 
parapet walls not less than 8 inches in thickness and carried 
2 feet above the roof, but for warehouses, factories, stores, and 
other buildings used for commercial or manufacturing purposes 
the parapet walls shall be not less than 12 inches in thickness and 



272/ DEFINITIONS OF THE TERMS USED IN MASONRY. 

carried 3 feet above tlie roof, and all such walls shall be coped 
with stone, terra-cotta, or cast iron. 

Sec. 44. Hollow Walls. — In all walls that are built hollow 
the same quantity of stone, brick, or concrete shall be used in 
their construction as if they were built solid, as in this Code pro- 
vided, and no hollow wall shall be built unless the parts of same 
are connected by proper ties, either of brick, stone, or iron, placed 
not over 24 inches apart. 

Sec. 45. Hollow Bricks on Inside of Walls. — The inside 
4 inches of all walls may be built of hard-burnt hollow brick, 
properly tied and bonded into the walls, and of the dimensions of 
ordinary bricks. Where hollow tile or porous terra-cotta blocks 
are used as lining or furring for walls, they shall not be included 
in the measurement of the thickness of such walls. 

Sec. 46. Recesses and Chases in Walls. — Recesses for 
stairways or elevators may be left in the foundation or cellar 
walls of all buildings, but in no case shall the walls be of less 
thickness than the walls of the fourth story, unless reinforced by 
additional piers with iron or steel girders, or iron or steel columns 
and girders, securely anchored to walls on each side. Recesses 
for alcoves and similar purposes shall have not less than 8 
inches of brickwork at the back of such recesses, and such 
recesses shall be not more than 8 feet in width, and shall be 
arched over or spanned with iron or steel lintels, and not carried 
up higher than 18 inches below the bottom of the beams of the 
floor next above. No chase for water or other pipes shall be 
made in any pier, and in no wall more than one third of its thick- 
ness. The chases around said pipe or pipes shall be filled up 
with solid masonry for the space of 1 foot at the top and 
bottom of each story. No horizontal recess or chase in any wall 
shall be allowed exceeding 4 feet in length without permission 
of the Commissioner of Buildings having jurisdiction. The 
aggregate area of recesses and chases in any wall shall not exceed 
one fourth of the whole area of the face of the wall on any story, 
nor shall any such recess be made within a distance of 6 feet from 
any other recess in the same wall. 

Sec. 47. Furred Walls. — In all walls furred with wood the 
Ijrickwork between the ends of wood beams shall project the 
thickness of the furring beyond the inner face of the wall for the 
full depth of the beams. 

Sec. 48. Light and Vent Shafts. — In every building here- 
after erected or altered all the walls or partitions forming interior 



DEFINITIOKS OF THE TERMS USED IK MASONRY. 2T2^ 

light or vent shafts shall be built of brick or such other fireproof 
materials as may be approved by the Commissioner of Buildings 
having jurisdiction. The walls of all light or vent shafts, 
whether exterior or interior, hereafter erected, shall be carried up 
not less than 3 feet above the level of the roof, and the brick 
walls coped as other parapet walls. Vent shafts to light interior 
bathrooms in private dwellings may be built of wood, filled in 
solidly with brick or hard-burnt clay blocks, when extending 
through not more than one story in height and carried not less 
than 2 feet above the roof, covered with a ventilating skylight of 
metal and glass. 

Sec. 49. Brick and Hollow Tile Partitions. — Eight-inch 
brick and 6-inch and 4-inch hollow tile partitions of hard-burnt 
clay or porous terra cotta may be built, not exceeding in their 
vertical portions a measurement of 50, 86, and 24 feet respect- 
ively, and in their horizontal measurement a length not exceeding 
75 feet, unless strengthened by proper cross- walls, piers, or but- 
tresses, or built-in iron or steel framework. All such partitions 
shall be carried on proper foundations, or on iron or steel girders 
or on iron or steel girders and columns or piers of masonry. 

Sec. 50. Cellar Partitions in Residence Buildings. — One 
line of fore and aft partitions in the cellar or lowest story, sup- 
porting stud partitions above, in all residence buildings over 20 
feet between bearing walls in the cellar or lowest story, hereafter 
erected, shall be constructed of brick not less than 8 inches thick, 
or piers of brick with openings arched over below the under side 
< ^f the first tier of beams, or girders of iron or steel and iron col- 
umns, or piers of masonry may be used ; or if iron or steel floor 
beams spanning the distance between bearing walls are used of 
adequate strength to support the stud partitions above in addition 
to the floor load to be sustained by the said iron or steel beams, 
then the fore and aft brick partition, or its equivalent, may be 
omitted. 

Stud partitions which may be placed in the cellar or lower 
story of any building shall have good solid stone or brick founda- 
tion walls under the same, which shall be built up to the top of 
the floor beams or sleepers, and the sills of said partitions shall 
be of locust or other suitable hard wood ; but if the walls are 
built five inches higher of brick than the top of the floor beams or 
sleepers, any wooden sill may be used on which the studs shall 
be set. 

Sec, 51. Main Stud Partitions. — In residence buildings 



2^2h DEFIKITIONS OF THE TERMS USED INT MASONRY. 

where fore and aft stud partitions rest directly over each other, 
they shall run down between the wood floor beams and rest on 
the top plate of the partition below, and shall have the studding 
filled in solid between the uprights to the depth of the floor 
beams, with suitable incombustible materials. 

Sec. 52. Timber in Walls Prohibited. — No timber shall be 
used in any wall of any building where stone, brick, or iron is 
commonly used, except inside lintels, as herein provided, and 
brace blocks not more than 8 inches in length. 



Safe Working Loads for Masonry. 

Brick Masonry in Walls or Piers. 

Tons per Sq. Ft. 

Hard brick in lime mortar 5 to 7 

'* ** ** Rosendale cement 1 to 3 8 " 10 

Pressed brick in lime mortar. ... 6 ** 8 

" " ** Roseudale cement 9**12 

** Portland " 12**15 

Piers exceeding in height six times their least dimension 
should be increased 4 inches in size for each additional 6 feet. 

According to the New York Building Lnws, brickwork in good 
lime mortar 8 tons per sq. ft., Hi tons when good lime and 



MASOJ!;rRY.— SAFE WORKING LOADS FOR MASONRY. 273 

cement mortar is used, and 15 tons when good cement mortar is 
used. 

According to the Boston Building Laws : 
Best hard-burned brick (height less than six times 
least dimension) with 

lbs. per Sq. Ft. 

Mortar, 1 cement, 2 sand 30,000 

1 *' 1 lime, 3 '* 24,000 

lime 16,000 

6est hard-burned brick (height six to twelve times 
least dimension) with 

Mortar, 1 cement, 2 sand 26,000 

1 '* llime,3 '' 20,000 

lime 14, 000 

For light hard-burned brick use f the above amounts. 

Stone Masonry. 

Tons per Sq. Ft 

jRubble walls, irregular stones 3 

** ** coursed, soft stone 2^ 

*' *' hardstone 5 to 16 

Dimension stone in cement: 

{Sandstone and limestone 10 " 20 

Granite 20 ** 40 

iOressed stone, with f-inch dressed joints, in 
cement : 

Granite 60 

Marble or limestone 40 

Sandstone .... , 30 

Height of columns not to exceed eight times least diameter. 

Mortars. 

Tons per Sq. Ft. 
In J inch joints 3 months old : 

Portland cement 1 to 4 40 

Rosendale ** 1 *' 3 13 

Lime mortar 8 to 10 

Portland 1 to 2 in :J-inch joints for bedding iron plates ... 70 

Concrete. 

Tons per Sq. Ft. 

Piyftland cement 1 to 8 , 8 to 20 

Rosendale ** 1 *' 6 5 '* 10 

Lime, best, 1 to 6 , 5 



274 MASONRY. — DESCRIPTION OF ARCHES. 

Hollow Tile. 

Pounds 
per Sq. Ft. 

Hard fire-clay tiles ; 80 

** ordinary clay tiles 60 

Porous terra-cotta ** 40 

Terra-cotta blocks, unfilled, 10,000 

** ** filled solid with brick or cement.. 20,000 



Description of Arches. 

Basket-handle Arch : One in which the intrados resembles 
a semi-ellipse, but is composed of arcs of circles tangent to each 
other. 

Catenarian Arch : One whose intrados is a catenary. 

Circular Arch : One in which the intrados is a part of a 
circle. 

Discharging Arch : An arch built above a lintel to take the 
superincumbent pressure therefrom. 

Elliptical Arch : One in which the intrados is a part of an 
ellipse. 

Geostatic Arch : An arch in equilibrium under the vertical 
pressure of an earth embankment. 

Hydrostatic Arch : An arch in equilibrium under the ver- 
tical pressure of water. 

Inverted Arches are like ordinary arches, but are built with 
the crown downwards. They are generally semicircular or seg- 
mental in section, and are used chiefly in connection with foun- 
dations. 

Plain or Rough Arches are those in which none of the bricks 
cut to fit the splay. Hence the joints are quite close to each 
other at the soffit, are wider towards the outer curve of the arch ; 
they are generally used as relieving, trimmer, tunnel-lining, and 
all arches where strength is essential and appearance no particular 
object. In constructing arches of this kind it is usual to form 
them of two or more four-inch concentric rings until the required 
thickness is obtained. Each of the successive rings is built inde- 
pendently, having no connection with the others beyond the ad- 
hesion of the mortar in the ring-joint. It is necessary that each 
ring should be finished before the next is commenced ; also that 
each course be bounded throughout the length of the arch, and 



MASONKY. — ARCHES. 275 

that the riug-joint should be of a regular thickness. For if one 
ring is built with a thin joint and another with a thick one the 
one having the most mortar will shrink, causing a fracture and 
depriving the arch of much of its strength. 

Pointed Arch : One in which the intrados consists of two 
arcs of equal circles intersecting over the middle of the span. 

Relieving Arch : See Discharging Arch. 

Right Arch : A cylindrical arch^ either circular or elliptical, 
terminated by two planes, termed "heads of the arch, at right 
angles to the axis of the arch. 

Segmental Arch : One whose intrados i^ less than a semi- 
circle. 

Semicircular Arch : One whose intrados is a semicircle ; 
also called n. full-centred arch. 

Skew Arch : One whose heads are oblique to the axis. Skew 
arches are quite common in Europe, but are rarely employed in 
the United States ; and in the latter when an oblique arch is em- 
ployed it is usually made, not after the European method with 
spiral joints, but by building a number of short right arches or 
ribs in contact with each other, each successive rib being placed d 
little to one side of its neighbor. 



Definitions of Parts of Arches. 

Abutment : The outer wall that supports the arch, and which 
connects it to the adjacent banks. 

Arch-sheeting : The voussoirs which do not show at the end 
of the arch. 

Camber is a slight rise of an arch, as J to J inch per foot of 
span. 

Crown : The highest point of the arch. 

ExTRADOS • The upper and outer surface of the arch. 

Haunches : The sides of the arch, from the springing-line half- 
way up to the crown. 

Heading-joint : A joint in a plane at right angles to the axis 
of the arch. It is not continuous. 

Intrados or Soffit : The under or lower surface of the 
arch. 

Invert : An inverted arch, one with its intrados below the 
axis or springing-line ; e. g., the lower half of a circular sewer. 

Keystone : The centre voussoir at the crown. 



276 MASOiiTRY. — CONSTRUCTION OF ARCHES. 

Length : The distance between face-stones of the arch. 

Pier : The intermediate support for two or more arches. 

Ring- COURSE : A course parallel to the face of the arch. 

Ring- STONES : The voussoirs or arch-stones which show at the 
ends of the arch. 

Rise : The height from the sp ringing-line to under side of the 
arch at the keystone. 

Skew-back : The upper surface of an abutment or pier from 
which an arch springs ; its face is on a line radiating from centre 
of arch. 

Span : The horizontal distance from springing to springing of 
the arch. 

Spandrel : The space contained between a horizontal line 
drawn through the crown of the arch and a vertical line drawn 
through the upper end of the skew-back. 

Springing : The point from which the arch begins or springs. 

Springer : The lowest voussoir or arch-stone. 

String-course : A course of voussoirs extending from one 
end of the arch to the other. 

Voussoirs : The blocks forming the arch. 



Construction of Arches. 

In constructing ornamental arches of small span the bricks 
should be cut and rubbed with great care to the proper splay or 
wedge like form necessary, and according to the gauges or reg- 
ularly measured dimensions. 

This is not always done, the external course only being rubbed, 
so that the work may have a pleasing appearance to the eye, while 
the interior, which is hidden from view, is slurred over, and in 
order to save time many of the interior bricks are apt to be so cut 
away as to deprive the arch of its strength. This class of work 
produces cracks and causes the arch to bulge forward, and may 
cause one of the bricks of a straight arch to drop down lower 
than the soffit. 

In setting arches the mason should be sure that the centres are 
set level and plumb, that the arch-brick or -stone may rest upon 
them square. When the brick or stone are properly cut before- 
hand the courses can be gauged upon the centre from the key 
downwards. The soffit of each course should fit the centre per- 
fectly. 



MASONRY. — CENTRING FOR ARCHES. 277 

The mortar-joints should be as thin as possible and well flushed 
up. 

In setting the face-stones it is necessary to have a radius-line, 
and draw it up and test the setting of each stone as it is laid. 

The framing, setting up, and striking of the centres are very 
important parts of the construction of any arch, particularly one 
of long span. A change in the shape of the centre, due to insuf- 
ficient strength or improper bracing, will be followed by a change 
in the curve of the intrados, and consequently of the line of resist- 
ance, which may endanger the safety of the arch itself. 



Centring for Arches. 

No arch becomes self-supporting until keyed up, that is, until 
the crown- or keystone-course is laid. Until that time the arch- 
ring, which should be built up simultaneously from both abut- 
ments, has to be supported by frames called centres. These con- 
sist of a series of ribs placed from 3 to 6 or more feet apart, 
supported from below. The upper surface of these ribs is cut 
to the form of the arch, and over these a series of planks called 
laggings are placed, upon which the arch-stones directly rest. 
The ribs may be of timber or iron. They should be strong and 
stiff. Any deformation that occurs in the rib will distort the 
arch, and may even result in its collapse. 

Striking the Centre. — The ends of the ribs or centre-frames 
usually rest upon a timber lying parallel to, and near, the spring- 
ing- line of the arch. This timber is supported by wedges, pref- 
erably of hardwood, resting upon a second stick, which is in turn 
supported by wooden posts, usually one under each end of each 
rib. The wedges between the two timbers, as above, are used in 
removing the dentre after the arch is completed, and are known 
as striking -wedges. They consist of a pair of folding w^edges, 1 to 
2 feet long, 6 inches wide, and having a slope of from 1 to 5 to 1 
to 10, placed under each end of each rib. It is necessary to re- 
move the centres slowly, particularly for large arches; and hence 
the striking-wedges should have a very slight taper, the larger the 
span the smaller the taper. 

The centre is lowered by driving back the wedges. To lower 
the centre uniformly the wedges must be driven back uniforml3^ 
This is most easily accomplished by nmking a mark on the side of 



278 MASOKEY. — CENTRING FOR ARCHES. 

each pair of wedges before commencing to drive, and then moving 
each the same amount. 

The inclined surfaces of the wedges should be lubricated when 
the centre is set up, so as to facilitate the striking. 

Screws may be used instead of wedges for lowering centres. 

Sand is also employed for the same purpose. The method 
followed is to support the centre-frames by w^ooden pistons or 
plungers resting on sand confined in plate-iron cylinders. Near 
the bottom of each cylinder there is a plug which can be with- 
drawn and replaced at pleasure, thus regulating the outflow of 
the sand and the descent of the centre. 

There is great difference of opinion as to the proper time for 
striking centres. Some hold that the centre should be struck as 
so :m as the arch is completed and the spandrel-filling is in place ; 
while others contend that the mortar should be given time to 
harden. It is probably be^t to slacken the centres as soon as the 
keystone-course is in place, so as to bring all the joints under 
pressure. The length of time which should elapse before the cen- 
tres are finally removed should vary with the kind of mortar em- 
ployed and also with its amount. In brick and rubble arches 
a large proportion of the arch-ring consists of mortar, and if the 
centre is removed too soon the compression of this mortar might 
cause a serious or even dangerous deformation of the arch. Hence 
the centres of such arches should remain until the mortar has not 
only set, but has attained a considerable part of its ultimate 
strength. 

Frequently the centres of bridge-arches are not removed for 
three or four months after the arch is completed, but usually the 
centres for the arches of tunnels, sewers, and culverts are removed 
as soon as the arch is turned and, say, half of the spandrel-filling 
is in place. 



CARPENTRY o — INSPECTION OF CARPENTRY. 279 



rV. CARPENTRY. 

Inspection of Carpentry. 

The inspection of carpentry requires the examination (1) of 
the material as to quality and dimensions ; (2) of the workman- 
ship in framing and placing it. 

In the interior work of buildings there are many points to be 
watched, as the placing of centres for arches, the setting of lintels, 
wood bricks, furrings, grounds, etc., the framing and trimming 
around chimneys and openings in floors and roofs, the laying 
and nailing of flooring, the jointing and setting of the standing 
trim, etc. 

The setting of window and door-frames requires precision on 
the part of the workman to make them plumb and securely 
fasten them, and the stuff used must be perfectly seasoned or the 
best workmanship will be thrown away. 

The hanging of doors requires considerable care so that they may 
move freely without causing any injurious strains in the hinges. 
Door-locks and -knobs require to be carefully fixed so they may 
work satisfactorily. The striking-plate is liable to be carelessly 
placed, being set either too high or too low or too far in the re- 
bate, so that either the latch or the bolt will not enter the mortise 
intended for it. The "roses" or round plates screwed on op- 
posite sides of the door, in which the stems of the knobs move, 
are rarely placed opposite to each other, so that the spindle, in- 
stead of being perpendicular to the door, is forced in an oblique 
direction, causing the knobs to bind and stick in turning. The 
knobs are frequently put on without the proper number of the 
thin washers which slip over the spindle for the purpose of filling 
out the space between the lock and the knobs on each side, and 
the latter are loose in consequence. 

The setting of window-sashes requires care ; nothing short of an 
actual trial of each sash of every window will serve to insure that 
all are as they should be. 



280 CARPENTRY. — JOINTS. 



Joints. 

In executing all kinds of joints in timber the following gen- 
eral principles are to be adhered to as closely as may be practi- 
cable : 

1. To cut the joints and arrange the fastenings so as to weaken 
the pieces of timber that they connect as little as possible. 

2. To place each abutting surface in a joint as nearly as possi- 
ble perpendicular to the pressure it has to transmit. 

3. To form and fit accurately every pair of surfaces that come 
in contact. 

Beams are joined in the direction of their length by the opera- 
tion called splicing, and the joints so formed are described as 
*' lapping," *' fishing," and '' scarfing." 

Fishing. — The ends of the pieces are butted together, and an 
iron or wooden plate or '* fish-piece" is placed on each side 
and fastened by bolts passing through the beam. 

The bolts should be placed checker -wise, so that the fish-plates 
and timbers are not cut through by more than one bolt-hole at 
any cross-section. 

Lapping is performed in a variety of ways, either by simply 
laying one beam over the other for a certain length and fastening 
them together with bolts or straps, or by halving and dovetailing 
the lapped portions. 

Scarfing consists in cutting away equally from the ends, but 
on the opposite sides, of two pieces of timber for the purpose of 
connecting them lengthwise. The form given to the scarf is 
varied to suit the nature of the strain it has to bear. 

Much ingenuity has been expended in devising scarfs of very 
intricate form, but the simplest are the best, as they are the 
easiest to fit accurately together. 

Halving is the simplest mode of joining timbers either length- 
wise or crosswise. Half the thickness of each piece is cut out 
and the remaining portion of one just fits into the other, the 
upper and under surfaces of the pieces being flush. This is a 
common way of joining wall-plates and other timbers at an angle 
where there is no room to let the ends project so as to cross one 
another. 

Bevelled halving : in this form the sides of the checks are splayed 
up and down. 

Doviiail halving^ so called from the shape of the pieces cut to 



CARPENTRY.— JOINTS. 281 

fit one another. They are objectionable in heavy limbers, be- 
cause the wood shrinks considerably more across the grain than 
along it ; the consequence is that they are easily drawn apart. 

Notching. — "When one beam rests upon another or crosses it 
the upper one is notched down upon the lower one, either to 
bring its surface to a given level or to aid in keeping it in phice . 
When the entire depth is cut from one beam it is termed *' single 
notching." When each timber is cut it is called *' double 
notching." 

Mortise and Tenon. — The mortise is a rectangular hole cut 
to receive the tenon, the sides of the mortise are called *' cheeks" 
The tenon is formed by dividing the end of the stick of timber 
into three parts, and cutting out on both sides rectangular pieces 
each equal to the part left in the middle. 

The tenon is usually made a little shorter than the depth of 
the mortise, so that the shoulders may bear firmly upon the tim- 
ber in which the mortise is cut. The tenon is fastened in the 
mortise by a wooden pin. The pin-hole is usually placed at ^ 
the length of the tenon from the shoulder, and is in diameter 
equal to \ the thickness of the tenon. 

The hole in the tenon is made slightly larger (in the direction 
of the length of the tenon), so that the pin when driven shall 
draw the tenon tightly into the mortise and cause the shoulders 
to butt close and make neat work. Care is required in driving 
the pin so that it will not draw too much and thus tear out the 
bit of the tenon beyond the pin. 

Double tenons are often used, but they should be avoided, as 
they weaken the timber into which they are framed, and both 
tenons seldom bear equally, so that a greater strain is thrown 
upon one of them than it is intended to support. 

Abutting Joint : A joint in which the fibres of one piece 
are perpendicular to those of the other. 

Butt-joint : A joint in which the pieces come square against 
each other endwise. 

Mitre : A joint where two pieces are framed together, 
matched, and united upon a line bisecting the angle of junction. 



282 CARPENTRY. — FLOORING. 



Flooring. 

Single flooring consists of a tier of joists running from one wall 
or partition to another without any intermediate support, and 
receiving the floor-boards on the upper edge, and the ceiling- 
joists, if there be one, on the lower edge. 

Double fljooring consists of girders, sometimes called ** binders," 
which support the floor-joists on their upper surface and the ceil 
ing- joists on their lower surface, or in some cases they are left 
exposed to view and the ceiling-laths nailed directly to the floor 
joists. 

Hardwood floors are laid either straight- joint or folding, and 
are ''edge-" or '' secret-nailed." In the folding method two 
boards are laid and nailed at such a distance apart that the space 
is a little less than the aggregate width of 3, 4, or 5 boards^ 
These boards are then put in their place, and on account of the 
narrowness of the space left for them they rise like an arch and 
require to be forced down into place. Accordingly the boards 
do not rest solidly upon the boards below, nor can the floor be 
laid with any degree of accuracy. This method should be 
avoided in good work. 

Straight- joint flooring is when every board is laid separately 
and blind or edge nailed ; any surface inequalities are reduced 
with the plane after the flooring is laid. 

It is of great importance that the rough flooring should be of 
narrow boards (about 4 inches wide) ; if wide boards are used 
each one of them in shrinking will gather up, so to speak, a 
cluster of the narrow hardwood pieces above it and draw them 
tightly together, and will transfer its shrinkage to the joints 
immediately over it, so that in a short time there will be a con- 
siderable space between the two floors, and the strain thrown on 
the thin edge of the grooves will cause them to curl up or split. 

It is usual before laying the finished flooring to spread upon 
the surface of the rough floor one, two, or three layers of felt 
paper to prevent air from passing through the joints and to 
deaden sound. Many and various qualities are manufactured, 
and care is required to see that the quality called for is furnished 
and tha^ it is carefully and evenly laid. 



CARPENTRY. — FLOORING. 283 



Parts of Floors 

Bay : The portion of a framed floor included between two 
girders, or a girder and a wal). 

A case-hay is the space between two girders. 

A tail bay is formed of common joists, where one end of each 
is framed into or supported by a header or girder. 

Binding- JOIST A joist whose ends rest upon the wall-plate 
and which supports the floor- joists above and the ceiling-joists 
below. 

Bridging. — By '' bridging" is meant a system of bracing floor- 
beams either by means of small struts set diagonally or by means 
of single boards set at right angles to the joists and fitting be- 
tween them. 

The ends of the bridging should be cut with exactly the same 
angle or bevel, so as to fit closely against the joist ; they should 
range in a straight line, so that none of their stiffening effect be 
lost. 

They should be fastened with two nails at each end, and care 
must be taken in nailing not to split them. To avoid this holes 
may be bored for the nails, or two small saw-cuts may be made 
to receive them. 

Single bridging, consisting of a single strut between the joists, 
is frequently used. Double bridging, consisting of two struts 
crossing each other, is the stiffer, and should always be em- 
ployed. 

Floor-beams. 

Joists. — The horizontal beams supporting floors and ceilings. 
Joists are usually spaced 12 inches centre to centre, and the ends 
rest upon wall-plates set in the walls. 

Trimming is the mode of framing around openings in floors, 
as where a chimney or stairway passes through. 

Trimmer-beams: The trimmer- or carriage-beams are those 
which support the header-beams. The headers are mortised into 
the trimmer- beams, or may be supported by iron beam-hangers 
fastened to the trimmer-beams. 

Header- BEAMS, or headers, are those which support the ends 
of the joist at one side of an opening. 

Tail-beams: The beams or joists supported at ea(!h end by a 
header-beam. 



284 CARPENTRY. — FLOORING. 

Regl'latioxs Xew York Building Code, 1899. 

Separation of Beams. — All wood beams and other timbers 
in the party wall of every building built of stone, brick, or iron 
shall be separated from the beam or timber entering in the oppo- 
site side of the wall by at least 4 inches of solid mason work. 

Bridging of Beams. — All wood floor and wood roof beams 
shall be properly bridged with cross bridging, and the distance 
between bridging or between bridging and walls shall not exceed 
8 feet. 

Dimensions of Beams. — All wood trimmer and header beams 
shall be proportional to carry with safety the loads they are in- 
tended to sustain. Every wood header or trimmer more than 
4 feet long, used in any building, shall be hung in stirrup- 
irons of suitable thickness for the size of the timbers. 

Thickness of Beams. — No wood floor beams or wood roof 
beams used in any building hereafter erected shall be of a less 
thickness than 3 inches. 

Bevelling Ends of Beams. — The ends of all wood floor and 
roof beams, where they rest on brick walls, shall be cut to a bevel 
of 3 inches on their depth. 

Bearing of Beams. — Every wood beam, except header and 
tail beams, shall rest at one end 4 inches in the wall, or upon 
a girder as authorized by this code. In no case shall either end 
of a floor or roof beam be supported on stud partitions, except 
In frame buildings. 

Trimmer Beams. — All wood beams shall be trimmed away 
from all flues and chimneys whether the same be a smoke, air, or 
any other flue or chimney. The trimmer beam shall not be less 
than 8 inches from the inside face of a flue and 4 inches 
from the outside of a chimney breast, and the header beam not 
L*ss than 2 inches from the outside face of the brick or stone 
work of the same; except that for the smoke flues of boilers and 
furnaces where the brickwork is required to be 8 inches in 
thickness, the trimmer beam shall be not less than l2 inches 
from the inside of the flue. The header beam, carrying the tail 
beam of a floor, and supporting the trimmer arch in front of a 
fireplace, shall be not less than 20 inches from the chimney 
breast. 

Anchors and Straps for Wood Beams and Girders.— 
Each tier of beams shall be anchored to tlic side, front, rear, or 



CARPENTRY. — FLOORlNa. 285 

party walls, at intervals of not more than 6 feet apart, with 
good, strong, wrought-iron anchors of not less than 1| inches 
by f of an inch in size, well fastened to the side of the beams 
by two or more nails made of wrought iron at least ^ of an inch 
in diameter. Where the beams are supported by girders, the 
girders shall be anchored to the walls and fastened to each other 
by suitable iron straps. The ends of wood beams resting upon 
girders shall be butted together end to end and strapped by 
wrought-iron straps of the same size and distance apart, and in 
the same beam as the wall anchors, and shall be fastened in the 
same manner as said wall anchors. 

Or they may lap each other at least 12 inches and be well 
spiked or bolted together where lapped. 

Each tier of beams front and rear, opposite each pier, shall 
have hard-wood anchor strips dovetailed into the beams diago- 
nally, which strips shall cover at least four beams and be 1 
inch thick and 4 inches wide, but no such anchor strips shall 
be let in within 4 feet of the centre line of the beams ; or 
wood strips may be nailed on the top of the beams and kept in 
place until the floors are being laid. Every pier and wall, front 
or rear, shall be well anchored to the beams of each story with 
the same size anchors as are required for side walls, which 
anchor shall hook over the fourth beam. 

Safe Load fok Wood Beams.— The safe carrying capacity 
of wood beams for uniformly distributed loads shall be deter- 
mined by multiplying the area in square inches by its depth in 
inches and dividing this product by the span of the beam in 
feet. This result is to be multiplied by 70 for hemlock, 90 for 
spruce and white pine, 120 for oak, and by 140 for yellow pine. 
The safe carrying capacity of short span timber beams shall be 
determined by their resistance to shear in accordance with the 
unit stresses fixed by section 139 of this code. 

Wood Columns and Plates. — All timber columns shall be 
squared at the ends perpendicular to their axes. 

To prevent the unit stresses from exceeding those fixed in this 
code, timber or iron cap and base plates shall be provided. 

Additional iron cheek plates shall be placed between the cap 
and base plates and bolted to the girders when required to trans- 
mit the loads with safety. 

Timber for Trusses. — When compression members of trusses 
are of timber they shnll b(; strained in the direction of tlie fibre 



2S5a CARPEKTR Y . — FLOORING. 

only. When timber is strained in tension, it shall be strained in 
the direction of the fibre only. The working stress in timber 
struts of pin- connected trusses shall not exceed 75 per cent of 
the working stresses established in section 139 this code. 

Bolts and Washers for Timber Work.— All bolts used in 
connection with timber and wood beam work shall be provided 
with washers of such proportions as will reduce the compression 
on the wood at the face of the washer to that allowed in section 
139 this code, supposing the bolt to be strained to its limit. 



286 CAEPEJSTTKY.— ROOFS. 



Roofs. 



The framing of roofs is determined by the drawings, but the 
material and workmanship require to be closely scrutinized to see 
that the framing is properly executed, that the various bolts, 
straps, and other fastenings are properly placed. The roof- 
boarding is to be inspected for quality; it should be planed 
smooth on one side, with smooth straight edges, and be free from 
loose knots. 

Parts of Roofs. 

Angle rafter : A rafter at the hip of a roof receiving the 
heads of the jack-rafters or cripple- studding. 

Arris-gutter : A V gutter fixed to the dripping- eaves of a 
roof. 

Barge-board : A board beneath the gable holding the hori 
zontal timbers. It is perforated, scalloped, or crenated to give it 
a light and ornamental appearance. 

Collar-beam : A horizontal piece of timber connecting and 
bracing two opposite rafters. 

Dragon-beam : A piece of timber to receive and support the 
foot of the hip-rafter. 

Hammer-beam : A tie-beam connecting the feet of a pair 
of principal rafters, but having its middle portion removed, the 
ends of the gap being staj^ed by ribs springing from corbels 
below. 

Eaves are the lower edges of the slopes of a roof. 

Facia-board : A board fixed to the ends of the rafters and to 
which the gutter is attached. 

Jack-rafter . One of the short rafters used in a hip-roof. 

King-post : A main post beneath the crown or ridge of a roof- 
frame. 

Purlin : A horizontal timber resting on a principal rafter. 

Queen-post : The post in a roof-truss placed between the 
ridge and the eaves. 

Rafter : One of the pieces of timber which follow the slope 
of a roof, and to which are attached the laths, boards, etc., 
which support the roof-covering. 

Ridge : The upper horizontal edge or comb of a roof. 

Ridge beam : A beam at the ii| pc:r edge of the rafters beneath 
the ridge. 



C ARPEIiTTRY. — STAIRS. 287 

Struts. —The posts or braces which run from the foot of the 
kiDg-post to the centre of the rafters. Struts, being under com- 
pression, should be made of full length and of well-seasoned 
wood ; otherwise upon shrinking they will allow the rafters to 
bend. 

Straining -BEAM : A beam used in a queen-post roof to keep 
the heads of the queen-posts apart. 

Tie-beam : The beam uniting the ends of a pair of principal 
rafters to prevent spreading. 

Tkimming : Wherever rafters come across any obstacle, such 
as a chimney, they must be trimmed in the same way as a floor. 

Wall-plates are the timber laid on the tops of walls to carry 
the foot of roof-trusses, rafters, or ends of tie-beams. They are 
usually fastened to the wall by iron anchor-bolts. 

At the angles of the walls the plates are halved or notched 
into one another, and well spiked together, and halved or scarfed 
wherever it is necessary to join them in the direction of their 
length ; they should be in long pieces, so as to avoid this as much 
as possible. 

Anchor-bolts should be built at every angle and at intervals 
of about ten feet. The bolts should be not less than one inch in 
diameter and three to four feet in length, with a square plate of 
iron at the lower end ; they should be built in vertically and so 
set that the threaded end may project at least an inch above the 
top of the wall-platCo In setting this holes are bored for the 
bolts, and nuts with large washers are put in and screwed down 
firmly. 

Stairs. 

The workmanship on stairs must be closely examined to insure 
that the treads and risers are properly framed and secured, that 
the risers are of proper height, and that the carriages or strings 
are properly set. Stairs of varying height or out of level are both 
iiangerous and unsightly. The wall-string must be carefully 
examined to see that it is securely fastened to the wall. 

The securing of the handrail must be carefully looked after. 
It frequently happens that the mortising or dovetailing of the 
balusters is dispensed with, nails driven through the tread 
being substituted ; this is a weak construction and should not be 
permitted. The securing of the end of a handrail which abuts 
against a wall is liable to be made in a shiftless manner unless 
specific directions are given for its proper securing. 



288 CARPENTRY. — STAIRS. 

Tlie risers are united to the treads by joints, which may be 
tongued and grooved or rebated ; in either case the joint is gUied 
and blocked. The riser often has only its upper end tongued, 
the lower butting upon the tread below. Tuis is not good con- 
struction. A comnion practice is to house the lower edge of the 
riser into the tread below. The tread is sometimes tongued into 
the riser, but this is not good construction. 

The joints between the tread and riser should be strengthened 
by small triangular or square bl ;cks glued in the angle. The 
inner ends of the treads where they rest upon the strings and also 
where they rest upon carriages should be supported by rough 
blocks or pieces of boards nailed to the strings and carriages. In 
some cases a board is notched out like a string and nailed 
along the side of the strings and carriages to answer for the rough 
blocks. 

In some cases the upper edge of the risers is housed or dove- 
tailed into the treads, and the back of the treads screwed up to 
the lower edge of the risers. 

Parts of Stairs. 

Baluster : Small pillar supporting a rail, as in a handrail. 

Balustrade : A railing composed of balusters. 

CARKixiGE OR String : One of the inclined pieces which sup- 
ports the steps of stairs. 

Flight is a continued series of steps without a landing. 

Handrail : The moulded rail parallel nearly throughout its 
length to the general inclination of the stairs. 

Landing is the flat resting-place at the top of any flight of 
stairs. 

Newel : The principal post at the angles and foot of a stairs. 

Nosing : The outer edge of the tread. In most cases it pro- 
jects beyond the face of the riser and is rounded or ornamented 
by a moulding. 

Rise : The vertical height between two treads. 

Riser is the face or vertical portion of the step. 

Strings. — The inclined pieces which support the steps of 
stairs. There are two classes — open strings, which are cut to 
show the outline of the steps ; close strings have their upper and 
lower surfaces parallel, the steps being housed into them. The 
wall string is the string placed against the wall and fastened to 
it. The outer string is the one fartl.est from the wall. In wide 
stairs which require more support than is afforded by the strings 



CARPENTIIY. — DOORS. 289 

one or more rough strings called carriages are placed between the 
wall-striijg aud viw. outer striug. 

Tread : The horizontal upper surface of a step. 

Winder : The triangular or tapering steps required in turning 
a corner or going round a curve. 

Doors. 

Hardwood Doors are usually veneered upon a core of well- 
seasoned pine to prevent warping. It is necessary to examine 
them upon delivery to see that the veneers are of the proper 
thickness and that the framing is properly executed. 

Pine and White-wood Doors intended for oil finish must be 
free from sap, knots, stain, pitch- streaks, and gum-spots, and 
finished with the grain. 

Parts op Doors. 

Panelled Doors consist of a framework of narrow pieces 
of equal thickness put together with mortise-and-tenon-joints and 
grooved on the inside to receive the panels. The parts of doors 
are designated as follows : 

Stiles : The vertical rails or bars. 

Hanging-stile : The stile to which the hinges are attached. 

Shutting- stile : The stile on which the lock is placed. 

Rails ; The horizontal bars of the framing, designated as the 
top-rail, frieze-rail, middle or lock rail, and bottom raiL 

Panelled doors are distinguished by different technical names 
expressing their thickness, the numberof panels they contain, and 
the kind of panelling. 

Panelling.— There are several forms of panels, known by 
technical names depending upon the manner in which they are 
respectively constructed and ornamented. 

Flush Panels have their surfaces ** flush" or in the same 
plane with the surface of the frame. A panel may be flush on 
one or both sides. 

Square and Floi Panels are those in which the boards are 
of the same thickness throughout, thinner than the frame, sunk 
square below its surface, and not ornamented by beads or 
mouldings. 

Moulded Square and Flat: When the edge of the- panel, 
close to the framing, is ornamented by a moulding either 
" planted " or ''stuck" on the inner edge of the frame. 



290 CARPEN^TRY. — STANDING FINISH OR TRIM. 

Beid-flush panels have a bead all round close to the inner 
edge of the fiaming. 

Bead and Butt : Framing in which the panels are flush 
and have beads stuck upon the two edges. 

Bead and Quirk: A bead stuck on the edge of a piece of 
stuff flush with its surface. 

Beady Butt, and Square : Framing with bead and butt on 
one side and square on the other. 

Solid Panels are tbose in which the panel is in one piece of 
the same thickness as the frame, and flush on both sides with its 
surface. 

Cliamfered Panel : The edges of the framing are cham- 
fered. 

Baised Panel has the surface nearly flush with the frame in 
the centre, but recessed back at the sides where it meets the 
frame. 

Panelling is often enriched with mouldings of different de- 
signs ; these are either " stuck " on the frame or " planted" in 
strips bradded on its inner side. Sometimes the panelling is re- 
quired to have a dift'erent appearance on each side. It is then 
formed differently on the two sides and named accordingly. 



Standing' Finish or Trim. 

Architraves are mouldings fixed round the openings of doors 
and windows for ornament and also to conceal the joint between 
the frame and the plastering. The architrave should be of well- 
seasoned wood, should be blind-nailed, and should not be fixed in 
place until the plastering is completed and quite dr3^ 

Base-board, Skirtings. — A board from 6 to 18 inches in width 
plticed round the base of the wall of a room, etc. The base-board 
may be plain or ornamented. 

The base-boards should be tongued or dovetailed and mitred at 
the internal angles. They should be tongued wherever they are 
pieced in length. They should be so fastened to the wall as to 
allow for contraction and expansion without splitting. 

The plastering behind the base-board should be carried down 
tight to the floor and no space left between the board and the 
wall. 

The base -board should be put in place before the finished floor- 
ing is laid ; in this way the base-board will extend below its sur- 



CARPEKTRY.— STANDING FINISH OR TRIM. 291 

face and thus can shrink without opening a crack between it and 
the floor. 

Linings are coverings of wood, usually some hard wood, so 
placed as to conceal or ornament portions of the interior of build- 
ings. There are several varieties of linings, distinguished by 
technical names denoting the position in which they are fixed, as 
jamb- and soffit-linings to doors and windows. 

All linings should be of narrow boards, ploughed, tongued, and 
grooved or rebated, so framed and nailed as to be free to expand 
and contract. Joints require careful attentioM in making, so that 
any shrinkage that may take place will not be visible. 

Mouldings are of various designs and are used merely for 
ornament. 

When a moulding is formed on the edge of a piece of timber in 
the substance of the wood itself it is said to be *' stuck." 

When it is on a separate slip of wood and attached to the piece 
it is to ornament it is said to be "laid in" or ** planted." 

In panelled work the mouldings are as a rule in separate slips, 
bradded or ''planted" on to the inner edges of the frames, not 
on the panels, as the shrinkage of the latter would draw them 
away from the frame. 

If, however, the moulding is ** stuck" on the frame the groove 
for the panel should be deeper than the moulding ; otherwise 
when the framing shrinks daylight will be seen through the open 
mitred corners of the moulding. 

Machine-wrought mouldings frequently have slight indenta- 
tions on the surface varying from a quarter to one third of an 
inch apart. These marks should be removed by sand-papering 
or if necessary by planing to prevent their showing after varnish- 
ing. 

Care is required in splicing mouldings to see that the adjoin- 
ing pieces are properly matched and that the joints do not come 
in prominent places. 

The wall-moulding, i. e., strips of moulding placed round the 
outside of architraves and linings, must be securely and neatly 
fastened. 

Wainscoting : A wooden facing about 3 feet high around the 
walls of rooms. 

Wainscoting, Filling Behind. — ''When wood wainscot- 
ing is used, in any building h^ireafter erected, the surface of the 
wall or partition behind such wainscoting shall be plastered 
down to the floor-line, and any intervening space between the 



293 CARPENTRY. — AYIN^DOAVS. 

said plastering and wainscot shall be filled in solid with incom- 
bustible material." (N. Y. Building Laws, 1896.) 

Windows. 

Windows consist of two parts : the sasli or sashes which, hold 
the glass, and the frame enclosing the sash. 

The frame in which the sash slides is either cased or solid. 
The former has boxes at each side for the weights. The latter 
consists of strips fastened to the window-jambs. 

A sash-casing consists of four pieces : the pulley-piece and in- 
side and outside and hack lining. The strips which form the sash- 
slides are the inside and outside heads and I he parti ng-&^acZ. 

The parts of a sash-frame are the head, sill, stool, and sides or 
casings. 

Frames require to be set plumb and securely fastened. If dur- 
ing the construction of the mason-work they get out of plumb 
they must be taken out and reset. After the frames are set 
pieces of boards should be nailed over the sills and if necessary 
on the sides to protect them from injury during the progress of 
the "work. 

The material used in the manufacture of tlie frames must be 
thoroughly seasoned and should be put together with paint made 
of 'inseed-oil and white lead. 

The top of the frame is sometimes covered with water-proof 
felt or a flashing of tin so as to prevent water from getting into 
the frames. 

Sashes. — The sashes are constructed like ordinary framing. 
The upright sides are the stiles, and the transverse or horizontal 
ones which are tenoned into the ends of the stiles are"the rails, and 
the interior pieces are the bars. If the bars are mitred at the 
joints they require dowels in the ends to act as tenons. 

The upper posts of the sashes have grooves taken out of their 
sides about J inch square and extending downwards about 6 
inches from the top, with a hole bored below it for 3 or 4 inches, 
wliich terminates in a large hole sunk in the side of tbe stile to re- 
ceive the ends of the sash-lines, which are secured by a knot and 
nailed ; these pass over iron or brass pulleys fixed in slots near the 
top of the pulley-stiles, and are attached to the weights which 
counterbalance the sashes. 

The weights are of cast iron, either circular or rectangular in 
section. In selecting them the sash is weighed and two weights 
are chosen which just balance the sash. 



CARPENTRY. — TERMS USED IN CARPENTRY. 293 

The weights are introduced through a rectangular hole formed 
in the pulley-stile. This bole is called the pocket and is covered 
by a flush cover, or pocket-piece. The upper end of this cover is 
usually rebated and undercut, and the lower end bevelled to fit 
snugly into the pulley-stile. There are various ways of makiog 
the joint, but in whatever manner it is made the ends of the cover 
should be fastened with brass screws. 

Terms used in Carpentry, 

Angle-staff : A strip of wood fixed to the vertical angle of 
a wall flush with the plastering of the two planes. It is designed 
as a substitute for plaster in a situation so much exposed. 

A round staff is known as an angle bead. 

Angle-tie : A brace in the interior angle of a wooden frame 
securing two side-pieces together and occupying thereto the posi- 
tion of a hypotenuse. 

AsHLARiNG : Short upright pieces between the floor-beams and 
rafters in garrets for nailing the laths to. 

Astragal ; (a) A small moulding of a semicircular section 
with a fillet beneath it ; (b) one of the rabbeted bars which hold 
the panes of glass in a window. 

Barge-couple : A beam mortised into another to strengthen 
the structure. 

Batten. — A strip of wood from J to 2J inches thick, and from 
1 to 7 inches wide. 

A cleat or bar nailed transversely on a structure of jointed 
planks, such as a door or shutter, to prevent warpinr;; and to pre- 
serve the relative position of the parts. 

A strip nailed to the rafters to which slates, etc., are nailed. 

A batten door is formed of planks laid side by side, and secured 
together by battens fastened across them without any exterior 
framing. 

Bead : A small convex moulding of semicircular section ; the 
circular portion is the bead, and the indentation on the side is 
called a quirk. 

Beam. — A straight stick of timber, usually occupying a rela- 
tively horizontal position in a structure. Specific denominations 
have been conferred upon beams in framed structures of wood, 
as ; 

Straining-beam : One used in a truss or frame to confine prin- 
cipal parts in place. 



204 CARPENTKY. — TERMS USED IN CARPENTRY. 

Truss-beam : The principal horizontal timbers of a truss, called 
tbe top and bottom chords, and from which proceed the stays 
and braces which hold and confer rigidity upon the frame. 

Arched Beam : A beam bent, cut, or built into an arched form. 

Built Beam : One made up of several parts scarfed or strapped 
together. 

Kerfed Beam : A beam whose under side has a number of trans- 
verse kerfs or saw-cuts penetrating to a certain depth, so as to en- 
able it to be bent. 

Beard : The sharp edge of a board. 

Bearer : A beam employed to carry other portions, as joists 
or short pieces to support gutters. 

Bevelling : The sloping of an arris ; removing the square 
edge. 

Bird's-mouth ! The notch at the foot of a rafter where it rests 
upon or against the plate. 

Block.— A square or triangular piece of wood fitted in the re- 
entering angle formed by the meeting of two pieces of board. 
The blocks are glued at the rear and strengthen the joint. 

Board. — A sawed piece of wood, relatively broad, long and 
thin, exceeding 4| inches in width and less than 2\ inches in thick- 
ness. The term plank is applied to a grade thicker than boards, 
though the two terms are often used indiscriminately. 

1. Clapboard, a rived slab of wood. 

2. Feather-edged, one edge thinner than the other. 

3. Listed, the sap-wood removed. 

4. Edge-shot, the edge planed true. 

5. Wrought, planed on one side. 

6. Matched, tongued and grooved. 

7. Jointed, lined and edge-planed so as to come together cor- 
rectly. 

Bolster : A horizontal cap-piece laid upon the top of a post 
or pillar to shorten the bearing of the beam or string-piece 
above. 

Box- frame : A casing behind a window-jamb for counterbal- 
ance-weights. 

Brace : A diagonal stay or scantling connecting the horizon- 
tal and vertical members of a truss or frame. 

Breast-summer : A beam inserted flush with the house-front 
which it supports, and resting at its ends upon the walls and at 
intermediate points upon pillars or columns. 



OARPE:NrTRY. — TERMS USED IN" CARPENTRY. 295 

Bridge-board : A notched board to which ihe treads and 
risers of a stair are fastened. 

Cap : The timber placed on the top of piles or posts. 

Chamfer.— A bevel or slope forward by cutting off the square 
edge of a board or beam. Stop- chamfer is one in which the 
chamfer is not carried to the extremity of the timber, but stopped 
and sloped or curved up at the end till it dies away again into the 
square angle. 

Clapboard. — A term irregularly used. It means : 

1. A weather-board on the side of a house, laid on lapping over 
the one below it. 

2. A roofing-board larger than a shingle, and not usually 
shaved. A common size is a riven board 48 inches long and 8 
inches broad. They are rived in the xiirection of the medullary 
rays, and the edge toward the heart is the thinner of the two. 

Cleat : A strip of wood secured to another to strengthen it. 

Corbel : A bolster ; a wooden supporting-piece or bracket. 

Crest : The ridge of a roof. 

Diagonals: Boards, etc., nailed on diagonally. 

Dado: A rectangular groove formed in a board with a tool 
called a dado-plane (see Housing). 

Dovetail : A flariog tenon adapted to fit into a mortise with 
receding sides to prevent withdrawal in the direction of the ten- 
sion it will be exposed to in the structure. 

Dowel : A pin used to connect adjacent pieces, penetrating a 
part of its length into each piece at right angles to the plane of 
junction. 

Draw-bore. — A hole so made through a tenon and mortise 
that the pin will draw up the shoulder to the abutment. The 
hole through the tenon is bored at a distance from the shoulder 
less than the thickness of the cheeks measured between the hole 
through the mortise and the face of the abutment against which 
the shoulder is drawn. 

Flatted : Timber that is hewn or sawn on two opposite sides 
only. 

FuRRiNGS are strips of wood nailed to joists, rafters, or walls 
to bring their surface to a uniform level before placing the laths 
for plastering. 

Gain : A notch made in the side of a timber to receive 
another. 

Housing consists in letting the whole end of one piece of tim- 
ber for a short distance into another. The groove or recess 



296 CARPEXTRY. — TERMS USED IX CARPENTRY. 

formed iu one piece is called the housing, and one piece is said 
to be boused or dadoed into tbe otber. 

Lintels : Sbort beams over tbe beads of doors and windows 
for supporting tlie superincumbent wall. 

Matched Boarding : Boards planed so as to form a close 
joint ; also applied to boards provided with a tongue and groove 
on opposite sides. 

Plate. — A beam on a wall or elsewhere to support other por- 
tions of a structure. Sill-plates are timbers laid upon foundation- 
walls. Floor-plates or interties are timbers which are framed 
into the studding, for the floor-beams to rest upon. Wall-plates 
are the timbers placed on top of the wall to support the ends of 
the roof. 

Plough Groove : A recess formed by a tool called a plough 
(see Dado). 

Rebate or Rabbet : A half groove along the edge of a 
board or moulding forming a longitudinal recess. 

Scantling : Lumber under 6 inches square. 

Scarf : A joint unitiug two pieces endwise. 

Seasoned , Dried lumber. 

Splice : A scarf-joint by which timbers are united for the 
purpose of lengthening them. 

Scribing ; Cutting the edge of a board to fit an irregular 
surface. 

Spline : A strip of wood or iron used instead of a tongue for 
driving iu the grooves of planks (used in sheet piling). 

Secret- or Blind-nailed ; Nails driven so that the heads 
are concealed, as in flooring nailed through the tongue. 

Shot : The edges of a board are said to be shot when it is 
planed perfectly straight. 

Stringer : A horizontal beam. 

Stud : The vertical piece in a stud partition. 

Stiles : The upright pieces of a door- or shutter- frame. 

Sill. — A sill iu framing is a timber which is laid across a tier 
of beams in order to receive the feet of the partition-studs. Mud. 
sill, the bottom timber in a trestle- bent. 

Tongue : A fin on the edge of a board adapted to fit into a 
groove on an aijacent board; called a tongue-and-groove joint 

Tongue, Spline, or Feather : A detached strip of wood or 
iron used instead of the tongue formed on the side of a plank for 
driving in the grooves formed in the plank (used chiefly iu sheet- 
piling). 



CARPENTRY.— TERMS USED IH CARPENTRY. 297 

Transom : A horizootal cross-bar or mullioii separating a door 
from a window over it; also applied to the window formed over 
a door. 

Upright r A pillar or post in a frame or structure. 

Veneered : Covered by a thin sheeting of ornamental wood. 

Wash-boards * The boards surrounding a room at the floor to 
a heighth of 6 to 18 inches (see Base-board and Skirtings). 

Weather-boarding : An outer covering of boards, which are 
generally'placed horizontally, so that the higher board overlaps to 
one below; sometimes they are placed vertically with battens over 
the joints. 

Wood Bricks are pieces of wood of the same thickness as 
bricks built into the walls as the work progresses for nailing the 
casings of doors, windows, etc., to. 



298 ERECTIOK OF IROK AND STEEL STRUCTURES. 



V. IRON- AND STEEL-WORK. 

Erection of Iron and Steel Structures. 

In erecting iron or steel structures care must be exercised to 
protect the material from injury by falls or heavy shocks. 

In bringing the several parts together for bolting or riveting 
the use of heavy mauls for driving should not be allowed. 
Wooden mauls should be used. Parts must not be forced to- 
gether, and any failure of members to come together properly 
must be noted and reported daily to the engineer or architect. If 
any difficulty arises which cannot be overcome by the ordinary 
appliances at hand it must be reported to the engineer before any 
radical measures are used to meet it. 

Special care must be exercised to keep columns plumb and the 
entire work in line. Probably the worst practice in the erection 
of architectural ironwork is the very common use of shims in 
the joints between the successive column-sections, thus concen- 
trating the loads on the opposite sides of the cross-section. The 
columns are usually kept iDlunib in this manner, but the practice 
is extremely vicious and should not be allowed. If the faces of 
the ends of the columns are properly planed or milled off, and 
the base plate set level, the use of shims will not be necessary. 
The greatest difficulty is in setting the base-plate in a truly hori- 
zontal plane. The ordinary carpenter's level is not sufficiently 
delicate; an engineer's level should be used. 

During wet weather the ironwork should be protected by 
water-proof canvas, tarred paper, or other material to prevent 
water from lodging in the concealed parts of the work. 

Rules, New York Building Code, 1899. 

Sec. 110. Skeleton Construction. — Where columns are used 
to support iron or steel girders carrying enclosure walls, the said 
columns' shall be of cast iron, wrought iron, or rolled steel, and on 
their exposed outer and inner surfaces be constructed to resist fire 
by having a casing of brickwork not less than 8 inches in thick- 



ERECTIOK OF TROX AN"D STEEL STRUCTURES. 299 

ness on the outer surfaces nor less than 4 inches in thickness on 
the inner surfaces and all bounded into the brickwork of the en- 
closure walls. The exposed sides of the iron or steel girders shall 
be similarly covered in with brickwork not less than 4 inches in 
thickness on the outer surfaces and tied and bonded, but the ex- 
treme outer edge of the flanges of beams, or plates or angles con- 
nected to the beams, may project to within 2 inches of the outside 
surface of the brick casing. The inside surface of girders may be 
similarly covered with brickwork, or if projecting inside of the 
wall, they shall be protected by terra-cotta, concrete, or other fire- 
proof material. Girders for the support of the enclosure walls 
shall be placed at the floor line of each story. 

Sec. 111. Steel and Wrought-iron Columns. — No part of 
a steel or wrought-iron column shall be less than ^ of an inch 
thick. No wrought-iron or rolled-steel column shall have an 
unsupported length of more than forty times its least lateral di- 
mension, or diameter, except as modified by section 138 of this 
Code, and also except in such cases as the Commissioner of Build- 
ings may specially allow a greater unsupported length. The ends 
of all columns shall be faced to a plane surface at right angles to 
the axis of the columns and the connection between them shall be 
made with splice plates. The joint may be effected by rivets of 
sufficent size and number to transmit the entire stress, and then 
the splice plates shall be equal in sectional area to the area of 
column spliced. When the section of the columns to be spliced 
are such that spliced plates cannot be used, a connection formed 
of plates and angles may be used, designed to properly distribute 
the stress. No material, whether in the body of the column or 
used as lattice-bar or stay-plate, shall be used in any wrought-iron 
or steel column of less thickness than one thirty-second of its un- 
supported width measured between centres of rivets transversely, 
or one sixteenth the distance between centres of rivets in the 
direction of the stress. Stay-plates are to have not less than four 
rivets, and are to be spaced so that the ratio of length by the least 
radius of gyration of the parts connected does not exceed forty; the 
distance between nearest rivets of two stayplates shall in this 
case be considered as length. Steel and wrought-iron columns 
shall be made in one- two- or three-story lengths, and the material 
shall be rolled in one length wherever practicable, to avoid in- 
termediate splices. Where any part of the section of a column 
projects beyond that of the column below, the difference shall 
be made up by filling plates secured to c( lunin by the proper num- 



300 ERECTION OF IROX AKD STEEL STRtJCTtTRES. 

ber of rivets. Shoes of iron or steel, as described for cast-iron 
columns, or built shoes of plates and shapes may be used, com- 
plying with same requirements. 

Sec. 112. Cast-ikon Columns.— Cast-iron columns shall not have 
less diameter than 5 inches or less thickness than J of an inch. Nor 
shall they have an unsupported length of more than twenty times 
their least lateral dimensions or diameter, except as modified by 
section 138 of this Code, and except the same may form part of an 
elevator enclosure or staircase, and also except in such cases as the 
Commissioner of Buildings having jurisdiction may specially allow 
a greater unsupported length. All cast-iron columns shall be of 
good workmanship and material. The top and bottom flanges, 
seats and lugs shall be of ample strength, reinforced by fillets and 
brackets; they shall be not less than 1 inch in thickness when 
finished. All columns must be faced at the ends to a true surface 
perpendicular to the axis of the column. Column joints shall be 
secured by not less than four bolts each not less than f of an inch in 
diameter. The holes for these bolts shall be drilled to a template. 
The core of a column below a joint shall not be larger than the 
core of the column above and the metal shall be tapered down for 
a distance of not less than 6 inches, or a joint plate may be inserted 
of sufficient strength to distribute the load. The thickness of 
metal shall be not less than one twelfth the diameter of the greatest 
lateral dimension of cross section, but never less than | of an incb. 
Wherever the core of a cast-iron column has shifted more than one 
fourth the thickness of the shell the strength shall be computed, 
assuming the thickness of metal all around equal to the thinnest 
part, and the column shall be condemned if this computation shows 
the strength to be less than required by this Code. Wherever blow- 
holes or imperfections are found in a cast-iron column which re- 
duces the area of the cross section at that point more than 10 per 
cent, such column shall be condemned. Cast-iron posts or columns 
not cast with one open side or back, before being set up in place, 
shall have a | of an inch hole drilled in the shaft of each post or 
column, by the manufacturer or contractor furnishing the same, 
to exhibit the thickness of the castings; and any other similar 
sized hole or holes which the Commissioner of Buildings may 
require shall be drilled in the said posts or columns by the said 
manufacturer or contractor at his own expense. 

Iron or steel shoes or plates shall be used under the bottom tier 
of columns to properly distribute the load on the foundation. 
Shoes shall be planned on top. ^ 



ERECTIOK OF IROK AND STEEL STKUCTURES. 301 

Sec. 113. Double Columns — In all buildings hereafter erected 
or altered, where any iron or steel column or columns are used to 
support a wall or part thereof, whether the same be an exterior or 
an interior wall, and columns located below the level of the side- 
walk which are used to support exterior walls or arches over ' 
vaults, the said column or columns shall be either constructed 
double, that is, an outer and an inner column, the inner column 
alone to be of sufficient strength to sustain safely the weight to be 
imposed thereon, and the outer columns shall be 1 inch shorter 
tlian the inner columns, or such other iron or steel column of suf- 
ficient strength and protected with not less than two inches of 
fireproof material securely applied, except that double or protected 
columns shall not be required for walls fronting on streets or 
courts. 

Sec. 114. Party- wall Posts. — If iron or steel posts are to be 
used as party posts in front of a party wall, and intended for two 
buildings, then the said posts shall not be less in width than the 
thickness of the party wall, nor less in depth than the thickness 
of the wall to be supported above. Iron or steel posts in front of 
side, division, or party walls shall be filled up solid with masonry 
and made perfectly tight between the posts and walls. Inter- 
mediate posts may be used, which shall be sufficiently strong, and 
the lintels thereon shall have sufficient bearings to carry the 
weight above with safety. 

Sec. 115. Plates Between Joints of Open-back Columns. 
— Iron or steel posts or columns with one or more open sides and 
backs shall have solid iron plates on top of each, excepting where 
pierced for the passage of pipes. 

Sec. 116. Steel and Iron Girders. — Rivets in flanges shall 
be spaced so that the least value of a rivet for either shear or 
bearing is equal or greater than the increment of strain due to the 
distance between adjoining rivets. All other rules given under 
riveting shall be followed. The length of rivets between heads 
shall be limited to four times the diameter. The compression 
flange of plate girders shall be secured against buckling, if its 
length exceeds thirty times its width. If splices are used, they 
shall fully make good the members spliced in either tension or 
compression. Stiffeners shall be provided over the supports and 
under concentrated loads ; they shall be of sufficient strength, as 
a column, to carry the loads, and shall be connected with a suffi- 
cient number of rivets to transmit the stresses into the web plate. 
Stiffeners shall fit so as to support tie flnnges of the girders. If 



301^ ERECTIOK OF IRON AND STEEL STRUCTURES. 

the unsupported depfh of the web plate exceeds sixty times its 
thickness, stiffeners shall be used at intervals not exceeding one 
hundred and twenty times the thickness of the web. 

Sec. 117. Rolled-steel aisd Wiiougiit-ikon Beams Used 
AS GiRDEES. — When rolled steel or wrought-iron beams are used 
in pairs to form a girder, they shall be connected together by bolts 
and iron separators at intervals of not more than 5 feet. All beams 
12 inches and over in depth shall have at least two bolls to each 
separator. 

Sec. 118. Cast-iron Lintels. — Cast-iron lintels shall not be 
used for spans exceeding 16 feet. Cast-iron lintels or beams shall 
be not less than f of an inch in thickness in any of its parts. 

Sec. 119. Plates Under Ends of Lintels and Girders. — 
When the lintels or girders are supported at the ends by brick 
walls or piers they shall rest upon cut granite or bluestone blocks 
at least 10 inches thick, or upon cast-iron plates of equal strength 
by the full size of the bearings. In case the opening is less than 
12 feet, the stone blocks may be 5 inches in thickness, or cast-iron 
plates of equal strength by the full size of the bearings may be 
used, provided that in all cases the safe loads do not exceed those 
fixed by section 139 of this Code. 

Sec. 120. Rolled- steel and Wrought-iron Floor and 
Roof Beams. — All rolled steel and wrought-iron floor and roof 
beams used in buildings shall be of full weight, straight and free 
from injurious defects. Holes for tie rods shall be placed as near 
the thrust of the arch as practicable. The distance between tie 
rods in floors shall not exceed 8 feet, and shall not exceed eight 
times the depth of floor beams 12 inches and under. Channels or 
other shapes where used as skewbacks shall have a sufficient 
resisting moment to take up the thrust of the arch. Bearing 
plates of stone or metal shall be used to reduce the pressure on 
the wall to the working stress. Beams resting on girders shall be 
securely riveted or bolted to the same ; where joined on a girder, 
tie straps of ^ inch net sectional area shall be used, with rivets or 
bolts to correspond. Anchors shall be provided at the ends of all 
such beams bearing on walls. 

Sec. 121. Templates Under Ends of Steel or Iron Floor 
Beams. — Under the ends of all iron or steel beams where thoy 
rest on the walls a stone or cast-iron template shall be built into 
the walls. Templates under ends of steel or iron beams shall be 
of such dimensions as to bring no greater pressure upon the brick- 
work than that allowed by section 1C9 of this Code. When rolled 



EKECTIOX OF IllOX AND STEEL STKUCTUKES. 30U 

iron or steel floor beams, not exceeding 6 inches in depth, are 
placed not more than 30 inches on centres, no templates shall be 
required. 

Sec. 122. Framing and Connecti Structural Work. — 
All iron or steel trimmer beams, headers, and tail beams shall be 
suitably framed and connected together, and the iron or steel 
girders, columns, beams, trusses, and all other iron work of all 
floors and roofs shall be strapped, bolted, anchored, and connected 
together, and to the walls. 

All beams framed into and supported by other beams or girders 
shall be connected thereto by angles or knees of a proper size and 
thickness, and have sufiicient bolts or rivets in both legs of each 
connecting angle to transmit the entire weight or load coming on 
the beam to the supporting beam or girder. In no case shall the 
shearing value of the bolts or rivets or the bearing value of the 
connection angles, provided for in section 139 of this Code, be 
exceeded. 

Sec. 123. Riveting of Structural Steel and Wrought- 
IRON Work. — The distance from centre of a rivet hole to the edge 
of the material shall be not less than — 

I of an inch for ^ inch rivets. 



¥ 




t 


H 


(( 


f 


i| 


<€ 


1 


li 


tl 


1 



Wherever possible, however, the distance shall be equal to two 
diameters. All rivets, wherever practicable, shall be machine 
driven. The rivets in connection shall be proportioned and placed 
to suit the stresses. The pitch of rivets shall never be less than 
three diameters of the rivet, nor more than 6 inches. In the direc- 
tion of the stress it shall not exceed sixteen times the least thick- 
ness of the outside member. At right angles to the stress it shall 
not exceed thirty-two times the least thickness of the outside 
member. All holes shall be punched accurately, so that upon 
assembling a cold rivet will enter the hole without straining the 
material by drifting. Occasional slight errors shall be corrected 
by reaming. The rivets shall fill the holes completely ; the heads 
shall be hemispherical and concentric with the axis of the rivet. 
Gussets shall be provided wherever required of suflftcient thick- 
ness and size to accommodate the number of rivets necessary to 
make a connection. 



301c EKECTio:Nr of irox and steel structures. 

Sec. 124. Bolting of Structural Steel and Wrought- 
IROX Work. — Where riveting is not made mandatory connections 
may be effected by bolts. These bolts shall be of wrought iron 
or mild steel, and they shall have U. S. Standard threads. The 
threads shall be full and clean, the nut shall be truly concentric 
with the bolt, and the thread shall be of sufficient length to allow 
tlie nut to be screwed up tightly. When bolts go through bevel 
flanges, bevel washers to match shall be used so that head and nut 
of bolt are parallel. When bolts are used for suspenders, the 
working stresses shall be reduced for wrought iron to 10,000 
pounds and for steel to 14,000 pounds per square inch of net area, 
and the load shall be transmitted into the head or nut by strong 
washers distributing the pressure evenly over the entire surface 
of the same. Turned bolts in reamed holes shall be deemed a 
substitute for field rivets. 

Sec. 125. Steel and Wrought-iron Trusses. — Trusses shall 
be of such design that the stresses in each member can be calcu- 
lated. All trusses shall be held rigidly in position by efficient 
systems of lateral and sway bracing, struts being spaced so that 
the maximum limit of length to least radius of gyration, estab- 
lished in section 111 of this Code, is not exceeded. Any member 
of a truss subjected to transverse stress, in addition to direct 
tension or compression, shall have the stresses causing such strain 
added to the direct stresses coming on the member, and the total 
stresses thus formed shall in no case exceed the working stresses 
stated in section 139 of this Code. 

Sec. 126. Riveted Steel and Wrought iron Trusses. — 
For tension members, the actual net area only, after deducting 
rivet holes, ^ inch larger than the rivets, shall be considered as 
resisting the stress. If tension members are made of angle irons 
riveted through one flange only, only that flange shall be con- 
sidered in proportioning areas. Rivets to be proportioned as 
prescribed in section 123 of this Code. If the axes of two adjoin- 
ing web members do not intersect within the line of the chords, 
sufficient area shall be added to the chord to take up the bending 
strains. No bolts shall be used in the connections of riveted 
trusses, excepting when riveting is impracticable, and then the 
holes shall be drilled or reamed. 

Sec. 127. Steel and Iron Pin-connected Trusses.— The 
bending stresses on pins shall be limited to 20,000 pounds for 
steel and 15,000 pounds for iron. All compression members in 
pin-connected trusses shall be proportioned, using seventy-five 



EKECTIOK OF IROlsr AKD STEEL STRUCTURES. 30 H^ 

per cent of permissible working stress for columns. The heads 
of all eye-bars shall be made by upsetting or forging. No weld 
will be allowed in the body of the bar. Steel eye-bars shall be 
annealed. Bars shall be straight before boring. All pin-holes 
sliall be bored true and at right angles to the axis of the mem- 
bers, and must fit the pin within ^^ of an inch. The distances 
of pin-holes from centre to centre for corresponding members 
shall be alike, so that, when piled upon one another, pins will pass 
through both ends without forcing. Eyes and screw end shall be 
so proportioned that upon test to destruction fracture will take 
place in the body of the member. All pins shall be accurately 
turned. Pin-plates shall be provided wherever necessary to 
reduce the stresses on pins to the working stresses prescribed in 
section 129 of this Code. These pin-plates shall be connected 
to the members by rivets of sufficient size and number to trans- 
mit the stresses without exceeding working stresses. All rivets 
in members of pin-connected trusses shall be machine driven. 
All rivets in pin-plates which are necessary to transmit stress 
shall be also machine driven. The main connections of members 
shall be made by pins. Other connections may be made by bolts. 
If there is a combination of riveted and pin-connected members 
in one truss, these members shall comply with the requirements 
for pin-connected trusses; but the riveting shall comply with the 
requirements of section 126 of this Code. 

Sec. 128. Iron and Other Metal Fronts to be Filled In. 
— All cast-iron or metal fronts shall be backed up or filled in 
with masonry of the thicknesses provided for in sections 31 
and 32. 

Sec. 129. Painting of Structural Metal Work.— All 
structural metal work shall be cleaned of all scale, dirt, and rust 
and be thoroughly coated with one coat of paint. Cast-iron 
columns shall not be painted until after inspection by the Depart- 
ment of Buildings. Where surfaces in riveted work come in 
contact, they shall be painted before assembling. After erection, 
all work shall be painted at least one additional coat. All iron 
or steel used under water shall be enclosed with concrete. 



302 FIRE-PROOF FLOORS. 

Fire-proof Floors. 

The term "fire-proof floor " is applied to floors constructed of 
fire-proof material supported on or between iron or steel beams 
or girders, or fire-proof walls, and entirely protecting the metal- 
work from the action of fire. 

The materials employed are ordinary building brick, hollow 
porous tile, hollow dense tile, thin plates of dense tile, iron in 
various forms imbedded in concrete composed of Portland 
cement and either cinders, broken stone, brick or tile ; and also 
compositions made with plaster of Paris as a cementing material. 

Brick Arches. — These usually consist of a single 4-inch course 
of brick with a rise at the centre of 3 or 4 inches (the preferable 
rise is not less than one-tenth of the span), resting either on the 
lower flanges of the I beams or on cast-iron or rolled- steel skew- 
backs fastened to the beams. If the floor is designed for very 
heavy loads several courses of brick are used. 

For first-class work the bricks should be ground to the taper of 
the arch, and be laid in place with as little mortar as possible. 

The space above the arch is usually filled in with concrete, in 
which are imbedded wooden strips 3x4 inches for securing the 
wooden flooring. 

The horizontal thrust of the arches is provided for by the use 
of tie-rods from f to 1 inch in diameter, spaced along the centre 
line of the beams or a little below, at regular intervals of from 5 
to 7 feet. The last rod is securely anchored to the wall, where 
an angle, channel, or simply a wall-plate is used to support the 
arch and to properly distribute the load upon the wall. 

In many cases where the arches abut against each side of the 

beam tie-rods are omitted, but it is always safer to use them, as 

the outside "bay" of the floor might be pushed off sidewise if the 

whole were not tied together ; also, if one of the arches should 

fall or break through, the rods would keep the other arches in 

place. 

Formula for Tie- rods for Beams supporting Brick 

Arches. — The horizontal thrust of brick is as follows : 

1 5 WS^ 
Pressure in pounds per lineal foot of arch = —^ — ^ . 

W = load in pounds per square foot. 
S = span of arch in feet. 
B = rise of arch in inches. 
Place the tie-rods as low through the webs of the beams as pos- 



FIRE-PROOF FLOORS. 303 

sible act! spaced so that the pressure of the arches as obtained by 
the above formula will not produce a greater stress than 15, OO'^ 
lbs. per square inch of the least section of the bolt. 

The beams supporting flat tile arches should invariably be 
bolted together with f-inch tie-rods, placed as near the bottom 
flange as practicable and drawn up tightly by nut and thread ; 
when so placed the floors are much stiffer and there is less lia- 
bility to cracks in ceilings than when the tie-rods are placed in 
the centre of the beams. The tie-rods should be spaced from 5 
to 7 feet, centre to centre. 

The formula for the diameter of the tie-rod for any floor is 

~ 62832r' 

2)2 = diameter of rod in inches. 

W= weight of floor and superimposed load resting on the 
arch, halfway between the tie-rods on each side, in pounds. 
S = span of arch in feet. 
r = rise of arch in feet. 

Hollow Tile. — These are furnished by the manufacturers in 
a great variety of patterns and of a strength to meet the desired 
requirements. Two general forms of construction are used, the 
segmental and the ''flat " arch. The flat arch usually has bevel 
joints ; radial joints are seldom used. Two methods of con- 
structing the flat arch are practised : one in which the blocks abut 
end to end continuously between the beams, and one in which 
they lie side by side, with broken joints between the beams. In 
the end system it is not usual to have the blocks in one row break 
joints with those in another, as it entails extra expense in setting. 
When it is done the strength of the floor is much increased. 

When dense tile are used they are backed up with concrete in 
which is imbedded the wooden strips for attaching the flooring. 
These strips should be of sound, seasoned wood, 2 inches thick 
by 2 inches wide on top, bevelled on each side to 4 inches wide 
on the bottom, placed about 16 inches between centres. The 
concrete should be firmly bedded beneath and against each side. 
When the finished floor is to be marble or tile the wooden strips 
are omitted. 

When porous tile is used they are generally made the full depth 
of the beam, the concrete backing being dispensed with, as they 
receive nails as readily as wood. 



304 



FIRE-PEOOr FLOORS. 



Laying Tile. — Id laying tile a mortar composed of lime mixed 
with coarse-screeued sand, in proportions of one to four, is used. 
A mortar-joint exceeding 4 inch in thickness should not be per- 
mitted. 

The best form of centring for flat arches is that in which T 
bolts are used, and double 2x6 inch sound lumber centre pieces 
below, placed midway between the beams and extending parallel 
with them, and like centre-pieces above, crossing the beams. The 
planks on which tiles are laid should be 2-inch, dressed on one 
eide to uniform thickness, and should lie on lower centres, at 
right angles to the beams and placed close together. The soffit- 
tile should be a separate key-slmped piece, of same width as the 
beam, and laid directly under the beam on the planking, after 
which the centring is tightened by screwing down the nuts on 
the T bolts, until the soffit-tile are hard against the beams and 
the planking has a crown not exceeding ^ inch in spans of six 
feet. 

The tiles should be laid " shoved," with close joints; and keys 
should fit close. 

The centres should remain in place from 12 to 36 hours, accord- 
ing to conditions of weather, depth of tiling, and kind of mortar 
used. 

When centres are *' struck," the ceiling should be straight, 
even, and free from open joints, crevices, and cracks. 

The laying of flat tile arches in winter weather without roof 
protection should not be practised in climates where frequent 
rain and snow storms are followed by hard freezing and thawing, 
as the mortar-joints are liable to be weakened or ruptured, re- 
sulting in more or less deflection of the arches. 

Table 59. 

WEIGHT AND SPANS OF FLAT HOLLOW DENSE-TILE ARCHES. 



Depth of 


Span between 


Weight per 


Arch. 


Beams. 


Square Ft. 


Inches. 




Pounds. 


6 


3.6" to 4.0" 


29 


7 


4.0 " 4.6 


32 


8 


4.6 " 5.6 


35 


9 


5.0 '^ 5.9 


37 


10 


5.9 '' 6.6 


41 


12 


6.6 " 7.6 


48 



FIRE-PKCOF FLOORS. 



305 



Table 60. 

WEIGHTS AND SPANS OF FLAT HOLLOW POROUS-TILE ARCHES. 



Depth of 


Span between 


Weight per 


Arch. 


Beams. 


Square Ft. 


Inches. 




Pounds. 


6 


3.0" to 5.0" 


21 


7 


3.6 '^ 5.6 


24 


8 


4.0 '^ 6.0 


27 


9 


. 4.6 '' 6.6 


30 


10 


5.0 '' 7.0 


33 


12 


6.0 '* 8.0 


37 


15 


7.6 ♦' 10.0 


43 



Six-inch hollow tile of either kind for segmental arches weigh from 26 to 
36 lbs. per square foot. 

Strength op Flat-tile Arches.— Flat arches should in all 
cases be capable of sustaining without serious deflection, after 
being set in place, an equally distributed load of 500 pounds per 
square foot of surface. 

Tests for Tile Floors. — Each arch shall be subjected to a 
test of a moving load consisting of a roller weighing 1000 pounds 
to each lineal foot, and applied 48 hours after the centres have 
been struck and before the concrete has been filled in. 

In addition to the rolling test, the arches after being set in 
place 72 hours shall be subjected to a dropping test made in the 
following manner : Before the concrete is applied on the arches 
a bed of sand two inches thick shall be spread loosely over the 
top of the arches, and a wooden block or timber weighing 200 
pounds shall be dropped thereon from a height of ten feet. If 
the arches withstand this impact for three continuous blows 
without breaking through, the test shall be considered satisfac- 
tory, and the floor arches be accepted. 

Concrete Floors. — There are several systems of construct- 
ing concrete floors. In some the concrete is supported on cor- 
rugated or other special forms of sheet iron ; in others the con- 
crete is emploj^ed as an arch, being made self-supporting by im- 
bedding in it iron or steel rods and bars of various forms. Metal 
lath, fand wire netting of various forms. Wire cables are also 
used. 

The various systems of concrete and composition flooring are 
in nearly all cases covered by patent, and full information con- 
cerning them can be obtained from the manufacturers. 



306 FIRE-PROOF FLOORS. 

Construction of Fireproof Floors. — New York Buildicg 
Laws, 1896; *'A11 brick or stone arches placed between iron or steel 
floor-beams shall be at least four inches thick and have a rise of at 
least one and a quarter inches to each foot of span between 
beams. Arches of over five feet span shall be properly increased 
in thickness, as required by the superintendent of buildings, or 
the space between the beams may be filled in with sectional 
hollow brick of hard-burned clay, porous terra-cotta, or some 
equally good fire-proof material, having a depth of not Jess than 
one and one-quarter inches to each foot of span, a variable distance 
being allowed of not over 6 inches in the span between beams. 
The said brick arches shall be laid to a line on the centres, with 
close joints, and the bricks shall be well wet, and the joints filled 
with cement mortar in proportions of not more than 2 of sand 
to 1 of cement by measure. The arches shall be well grouted 
and pinned or chinked with slate, and keyed. 

*' The bottom flanges of all wrought-iron or rolled-steel floor- 
beams, and all exposed portions of such beams below the abut- 
ments of the floor-arches, shall be entirely incased with hard-burnt 
clay or porous terra-cotta ; or with wire metal lath properly 
secured and plastered on the under side. The exposed sides and 
bottom plates or flanges of wrought iron, or rolled-steel girderg- 
supporting iron, steel, or wooden floor- beams, or supporting floor- 
arches or floors, shall be entirely incased in the same manner." 



EOOFIKG. — INSPECTION OF ROOFING. 307 



VI. Roofing-. 
Inspection of Roofing. 

The inspection of roofing requires considerable care because of 
the difSculty of detecting defects after the work is done until at- 
tention is called to them by damp walls or damaged ceilings. 

The first points to be examined are the quality and dimensions 
of the materials ; 2d, the quality of the workmanship in cutting, 
fitting, and placing the roof -frame, the laying of the sheathing, 
purlins, etc., and the laying, fastening, etc., of the roof-covering, 
and the forming of the flashings, gutters, connecting of leaders, 
etc. 

In slating, tiling, and shingling an important point is the 
sufliciency of the bond or lap. These materials are said to be laid 
so many inches to the weather, meaning the amount of the ex- 
posed portions. By increasing the length of the exposed portion, 
thus reducing the lap, a less number of courses will be required 
to cover the roof. 

The sheathing-boards should be sound, free from large knots, 
and well seasoned, laid with close joints in regular courses 
diagonally across the rafters and nailed with two nails to each 
bearing . All joints should be made in the centre of bearings, the 
ends of the boards being cut to the required angle. 

The sheathing-boards are usually covered with asphalted felt, 
tarred felt, or paper. In laying this material the joints should 
have a lap of 2 inches and be nailed at intervals of 2 or 3 inches 
with |-in. roofing-nails. One pound of nails should be allowed for 
each 100 square feet of roof. Dry or rosin-sized felt should not be 
used on roofs. 

On the completion of the roofing all accumulations of rubbish 
in the gutters must be cleared out, and nothing left to impede the 
flow of the water to the leaders. * 

Tin Roofing.— For laying on the roof the sheets of tin are 
joined together by having the edges bent in the form of a hook, 
called botli "single" and "double" groove o'- lock : t]>e sheets 
are hooked together, then hammered flut, and ihen boldeied. 8ev- 



30S HOOFING. — INSPECTIOK OF ROOFING. 

eral sheets are thus joiued and formed into a roll. The rolls are 
carried to the roof and spread out; their sides are joined by form- 
ing a single groove on each edge, flattened down, and soldered. 

In solderiog the joints, rosin as a flux is generally preferred, 
although some roofers recommend the use of dilute chloride of 
zinc. 

For a steep roof, tin should be put on with a standing groove 
and with the cross-seams double-locked and soldered. The tin 
should be laid with the smallest dimension for the width, as it 
makes the roof stronger, and allows a greater amount of expan- 
sion and contraction; but it is much cheaper to lay them the other 
way, as less cleats, solder, nails, and labor are required. For flat 
roofs with flat seams it does not make any difference which way 
the plates are laid, as the entire roof is practically a solid sheet. 

A very common and cheaper method for steep roofs is to dou- 
ble-lock both the vertical and cross seams, and fill the joints with 
white lead instead of soldering; but the other method is much 
the best. 

To hold the tin securely to the sheathing-boards, pieces of tin 
three or four inches long by two inches wide, called '* cleats," are 
nailed to the boards at about every eighteen inches along the 
joints of the rolls that are to be united, and are bent over with a 
double groove. They should be nailed with a fourpenny slating- 
nail, which has a broader head than common nails; and as the 
nails are not exposed to the weather, they may be of plain iron. 
The nails should not be driven through the roofing-plates. 

The under side of the tin should be painted before laying on 
the roof 

One or more layers of felt paper should be placed under the 
tin, to serve as a cushion, and also to deaden the noise produced 
by the rain striking the tin. 

Before painting all grease and rosin should be thoroughly 
scraped and cleaned off. 

The tin used for gutters and flashings should be of the heaviest 
coated or dipped plates and should always be of IX thickness. 

Roofing-tiles are thin slabs of baked clay. 

Plain roofing-tiles are usually made f of an inch in thickness, 
10^ inches long, ^id 6 J inches wide. They weigh from 2 to 2^ 
pounds each, and expose one half to the weather. Plain tiles are 
also made with grooves and fillets on the edges, so that the}^ are 
laid witliout overlapping very far. 

Pan-tiles have a wavy surfnce, lapping under and being over- 



ROOFIKG.— IKSPECTlOlsr OF ROOFIKG. 



309 



lapped by the adjacent tiles of the same course. They are made 
14i X 10^ iuches, expose 10 inches to the weather, and weigh 
from 5 to 5J pounds each. 

Tiles are laid in the same manner as slates, fastened with two 
nails to each tile. 

Crown-, ridge-, hip-, and valley-tiles are semi- cylindrical, or 
segments of cylinders, used for the purpose indicated by the name. 

Tiles should be well burned and be free from fire-checks, 
cracks, blisters, and flaws. 

Shingles. — The principal requisites of good shingles are 
freedom from knots, cross-grain, and an approximation to uni- 
form width. The wood usually employed for shingles is cedar, 
cypress, and Michigan piue (spruce is occasionally used ; but 
makes shingles of a very inferior quality). 

Shingles are usually laid in three thicknesses, except for an 
inch or two at the upper ends, where there are four. They are 
nailed to sawed shingling-laths of oak, spruce, or pine, about 16 
feet long, 2J inches wide, and 1 inch thick, placed in horizontal 
rows about 8J inches apart. Two oails are used for each shiugle, 
near its upper end ; they should not be of less size than 400 to a 
pound. Wrought nails are the best; cut nails are apt to break off 
by the warping of the shingles. 

Shingles are usually 27 inches long by from 6 to 7 inches wide, 
about I inch thick at the upper end, and about | inch at the lower 
end or butt, and are laid in courses exposing from 4 to 6 inches 
to the weather — One thousand shingles require about 5 lbs. of 
nails. 

Table 61. 

NUMBER AND WEIGHT OF SHINGLES (PINE) PER SQUARE. 



Number of Inches 
exposed to Weather. 


Number of Shingles 
per Square.* 


Weight per Square. 
Pounds. 


4 

r- 


900 
800 
720 
655 
600 


216 
192 
173 
157 
144 



* F&f hip-roofs add 5 per cent. 

Slates are laid either on a brca^i slieathing (rough or tongued 
an^l grooved) cover',! wit It taired paper or felt, or on rooting- 



310 ROOFIXG.~i:NrSPECTIOX OF ROOFING. 

laths, 2 to 3 iuches wide and from 1 to IJ iucbes thick, nailed t 
the rafters at distances apart to suit the gauge of the e^lates. 

The slates are fastened with two 3d. or 4d. nails, one near each 
upper corner. Copper, composition, tinned, or galvanized nails 
should be used. Plain iron nails are frequently used ; they 
are speedily weakened by rust, break, and allow the slates to be 
blown off. "When used they should be heated and immersed in 
boiled linseed-oil as a partial preservative from rust. 

On iron roofs slates are often placed directly on small iron 
purl ins spaced at suitable distance to receive them. There the slates 
are fastened with wire passed through the holes in the slate and 
twisted around the purlins. Special forms of fasteners are also 
used instead of wire. 

The gauge of a slate is the portion exposed to the weather. 
The slater estimates the length of the slate from the nail-hole to 
the tail, discarding the narrow strip between the nail-hole and 
I lie head. In order that the showing lower edge of the slates shall 
when laid form regular straight lines along the roof the nail- 
holes are made at equal distances from the lower edges. 

As the slates do not lie exactly parallel to the boarding, and 
consequently do not lie flat upon it, thoseat the lower edge would 
be easily broken. To prevent this a tilting -strip (a lath with its 
upper side planed to a bevel corresponding to the slope of the 
roof is first nailed at the eaves for the tail of the lowest course of 
slates to rest on. 

The upper side of a slate is called its hack, the lower one its bed. 

The area of roof covered by a slate of given dimensions is as- 
certained by multiplying the gauge by the width of the slate in 
iuches. 

Slates should be sorted in sizes when they are not all of one 
size, and the smallest placed near the ridge. 

The top course of slate on the ridge, and the slates for two to 
four feet from all gutters, and one foot each way from all valleys 
and hips, should be bedded in Portland-cement paste. 

In lading slates the great object to be attained is that the bottom 
edge or " tail " of every slate should fit as closely as possible to 
the backs of those below it. The vertical joints between the 
slates should be as close as possible, and each should fall on the 
central line of the slate below. 

In good slating the vertical joints of the alternate courses 
r.ho'ild rnnge in straiprht lines from ridge to caves, and the tails 
uf tbe slatL'S should be in perfectly horizontal lines. 



ROOFING. — INSPECTIOK OF ROOFING. 311 

Characteristics of Good Slates.— A good slate should be 
both hard and tough. 

Softness or liability to abrasion does not always indicate in- 
ferior roofing- si ate. A moderate degree of softness indicates 
good weathering qualities. 

If it is too soft, it will absorb moisture, the nail-holes will be- 
come enlarged, and the slate will become loose. 

If it be brittle, it will break in the process of squaring and 
holing. 

A good slate should give a sharp metallic ring when struck 
with the knuckles. It should not splinter under the slater's axe, 
should be easily " holed " without danger of fracture, and should 
not be tender or friable at the edges. 

A good roofing-slate should not absorb water to any percepti- 
ble extent. 

A common and easily applied test for roofing-slate is to place 
me on edge to half its depth in water, and if in, say, 12 hours the 
line of absorbed water approaches the top of the slate, it should 
be rejected. If it does not rise beyond one-eighth of an inch, the 
slate may be considered as practically nonabsorbent. 

Another method is to weigh a well -dried slate, and after soak- 
ing it for 12 hours in water to weigh again ; the difference in 
weight will show the quantity of water absorbed. 

A good slate after 12 hours' soaking in water should not have 
absorbed more than 3^^ part of its weight. 

As a test of the weathering quality it is recommended to 
breathe on the slate. If a clayey odor be strongly emitted, it is 
inferred that the slate will not *' weather " well. 

Notes on Slates. — (Northampton County (Pa.) Slate.)— The 
best slates are called *'No. 1 stock." Those with one ribbon 
crossing them are **No, 1 Rib," and those with two ribbous 
**No. 2 Rib." 

Ribbons are seams which traverse the slate in approximately 
parallel directions, and which differ in color and composition 
from the slates proper. In the upper beds the ribbons are soft 
and of inferior quality to the slate proper ; in the lower Ihey are 
often harder than the slates. 

Slates containing soft ribbons are inferior, and should not be 
used in good work. 

The soft slates weigh about 173 lbs. per cubic foot, and the 
best qnalilies have a modulus of rupture of from 7000 to 10,000 
lbs. per square inch. 



312 



ROOFING. — INSPECTION OF ROOFING. 



The stronger the slate the greater is its toughness and softness 
and the less its porosity and corrodibility. 

The strongest slate stands the weather best, so that a bending 
test affords an excellent index of all its properties. 

The strongest and best slate has the highest percentage of sili- 
cates of iron and aluminum, but is not necessarily the lowest in 
carbonates of lime and magnesia. 

Chemical analyses give only imperfect conclusions regarding 
either durability or physical properties. 

Bending tests should be required by the specifications. 

Slates are made in numerous sizes, varying from 6 X 12 to 16 
X 26 inches. In proper roofing a triple lap of 3 inches is al- 
lowed ; thus for a 24-inch slate 10^ inches of each slate are un- 
covered, 10 J inches are covered by one thickness, and 3 inches by 
two thicknesses. 

The amount of slate required to cover a space 10 X 10 feet is 
called a square. 

Table 62. 



SLATE. 
DIMENSIONS AND NUMBER PER SQUARE. 



Dimensions. 


Number per 


Dimensions. 


Number per 


Inches. 


Square. 


Inches. 


Square. 


6 X 12 


533 


12 X 18 


160 


7 Xl2 


457 


10 X 20 


169 


8 X 12 


400 


11 X 20 


154 


9 X 12 


355 


12 X 20 


141 


7X14 


374 


14 X 20 


121 


8 X 14 


327 


16 X 20 


137 


9X 14 


291 


12 X 22 


126 


10 X 14 


261 


14 X 22 


108 


8 X 16 


277 


12 X 24 


114 


9 X 16 


246 


14 X 24 


98 


10 X 16 


221 


16 X 24 


86 


9 X 18 


213 


14 X 26 


89 


10 X 18 


192 


16 X 26 


78 



Thickness i", y'g", J", increasing by eights to 1 inch. 

The weight of slate is about 174 pounds i^er cubic foot, or, per 
•^qiifire foot of various thicknesses, as follows : 
Tliickness, inches J j\ } ¥ i I J I 1 

Weight, pounds. 1.81 2.71 3.02 5.4:5 7.25 9.06 10.88 12.69 14 50 



ROOFING. — INSiMi:CTIO]Sr OF ROOFING. 



313 



Galvanized Iron. 



Galvanized iron, both flat and corrugated, is used for the roofs 
and sides of buildings. 

Flat iron is usually laid upou a sheathing of boards, but the 
strength of corrugated iron obviates the necessity for this. It is 
usually laid directly upon the purlins, and held in place by means 
of clips of hoop-iron, which encircle the purlin, and are spaced 
about 12 inches apart. 

The corrugated sheets are fastened togelher with rivets of 
galvanized wire about -J- inch in diameter ; the rivet-boles are 
spaced about 3 inches apart and are punched by machinery, so 
as to insure coincidence in the several sheets. The rivets must be 
well driven, so as to exclude rain, and the projecting edges at the 
eaves and gable-ends of the roof must be well secured, or the wind 
will loosen the sheets and fold them up. 

Table 63. 

GALVANIZED IRON. 

WEIGHT PER SQUARE FOOT. 



No. by 
Birming- 
ham Wire 

Gauge. 


Thick- 
ness in 
Inches. 


Flat. 
Lbs. 


Corru- 
gated. 
Lbs. 


No. by 
Birming- 
ham Wire 

Gauge. 

21 


Thick- 
ness in 
Inches. 


Flat. 1 
Lbs. 


Corru- 
gated. 
Lbs. 


30 


.012 


.806 


.896 


.032 


1.63 


1.81 


29 


.013 


.857 


.952 


20 


.035 


1.75 


1.94 


28 


.014 


.897 


.997 


19 


.042 


2.03 


2.26 


27 


.016 


.978 


1.09 


18 


.049 


2.32 


2.58 


26 


.018 


1.06 


1.18 


17 


.058 


2.68 


2.98 


25 


.020 


1.14 


1.27 


16 


.065 


2.96 


3.29 


24 


.022 


1.22 


1.36 


15 


.07-2 


3.25 


3.61 


28 


.025 


1.34 


1.49 


14 


.083 


3.69 


4.10 


22 


.028 


1.46 


1.62 


13 


.095 


4.18 


4.64 



Table 63«. 

SHOWING NUMBER OF GALVANIZED SHEETS GENERALLY 
PLACED IN BUNDLES. 







Width of Sheets in 


Inches. 




Thickness of 










Sheets. 


24 


26 


28 


30 


36 


No. 18 


5 


4 


4 


4 


Loose 


20 


6 


5 


5 


5 


4 


23 


7 


7 


6 


6 


5 


24 


10 


9 


8 


8 


6 


25 


10 


9 


8 


8 




26 


11 


10 


9 


9 


7 


27 


11 


10 


9 


9 




28 


12 


11 


10 


9 





T}ie standai'd diitien.sions of corrugated sliecls oro 26 inches wi<ic, C'>rni- 
gations 2J.^ inches wide Ijy % iTu;lj deep. Sheets No. 24 gauge and light.»r 
can l)e niacie with 1^ inch corrugations >4 '"ch deep. .Corrugations 114, 2, 
aud 3 inches are made to order. 



314 ROOFIKG. — COPPER roofi:n-g. 



Copper Roofing. 

The copper used for roofing usually weighs from 12 to 14 
ouDces per square foot. It is laid on boards in the same manner 
as tin except that solder is not used. The thin sheets are often 
found with slight cracks or flaws, which if used in roofing will 
soon cause it to become leaky. 

The weight of copper sheets used for flashing is from 12 to 18 
ounces per square foot. 



Table 64. 

APPROXIMATE WEIGHT OF VARIOUS ROOF- COVERINGS. 



( 



MatPrial Weight in Pounds per 

Material. Square of Roof. 

Yellow pine, Northern, sheathing, 1" thick 300 

Yellow pine, Southern, '* ** '* 400 

Spruce, *' '' '* 200 

Chestnut or maple, ** ** ** 400 

Ash or oak, *' ** *' 500 

Shingles, pine 200 

Slates i" thick 900 

Sheet iron ^V' ^liick 300 

** ** '' andlaths 500 

Iron, corrugated 100 to 375 

'* galvanized, flat 100*' 350 

Tin 70 '* 125 

Felt and asphalt 100 

Felt and gravel 800 * * 1000 

Skylights, glass yV' to I" thick 250 * ' 700 

Sheetlead 500 ** 800 

Copper 80 *' 125 

Zinc 100 *• 200 

Tiles, flat 1500" 2000 

** ** with mortar 2000" 3000 

«* pan 1000 



ROOFING. — FLASHIN'G, dlt 



Flashing. 



Flashing is the name given to the covering of the joint at the 
junction of a sloping roof and a wall or chimney. The material 
employed is tin, copper, zinc, and lead. The flashing is formed 
by bending the edge of the sheet of metal at right angles for one, 
two, or more inches, and inserting the portion so bent into the 
joints of the masonry, and is stepped down as the roof descends. 

Counter- or ca^-flashings are of tin, copper, or lead, and are laid 
between the courses in the masonry, and turned down over the 
ordinary flashing. In flashing against stonework small grooves or 
reglets often have to be cut to receive the ends of the counter- 
flashing. 

Flashing must be carefully executed to insure a tight roof. 

Gutters are metal troughs or wood troughs lined with metal, 
for the purpose of carrying off rain-water from roofs. They are 
of different forms, and should have a fall of 1 inch in 10 feet to 
the leader or pipe which conducts the water to the ground or 
drain. The metal used is either tin, galvanized iron, zinc, or 
lead. The sides of gutters which abut against walls should be 
turned up from 6 to 8 inches against them and be covered with an 
apron. In gutters formed along the eaves of roofs the metal 
should be turned up and extend upon the top of the roof-board- 
ing for not less than 10 inches and be securely nailed thereto. 

Yalleys are formed by the intersection of two roof -slopes 
forming a re-entering angle. They are made water-tight by 
covering with a flashing of tin, lead, or zinc, the sides of which 
are turned up along the roof boarding for a distance of from 5 lo 
7 inches. 

A '• close valley" is one in which the roof-covering is mitred 
and flashed in each course so that no metal can be seen. 

An ' ' open valley ' ' is one in which the metal is exposed to 
view in the finished roof. 

Suitable provision must be made for the expansion and con- 
traction of the metal used in valleys; when lead is used no sheet 
should be laid in a length greater than 10 feet without an ex- 
pansion-joint formed by a *'drip," "roll," or break of some 
kind. 

The joints of the metal sheets in ridges, hips, and valleys 
should have a lap of about 4 inches. 



316 



ROOFING. — FLASHING. 



The weight of lead used for flashings is usually 5 lbs. per 
square foot, for liips. ridges, aud small gutters 6 lbs., aod for flats 
aud main gutters 7 lbs. 

Tiie weight of copper used for cap-flashiug is usually sixteen 
ounces. 



PLUMBING. — INSPECTI0:N^ OF PLUMBING. 317 



VII. PLUMBING. 

Inspection of Plumbing^. 

The work of the plumber comprises the placing of the pipes 
and fittings required for the water-supply and the removal of 
sewage from buildings. Each municipality usually has regula- 
tions giving specific directions as to the manner in which the 
work must be executed. 

The duty of the inspector is : 

1. To examine the quality and dimensions of the materials to 
be used. 

2. To see that the work is executed in accordance with the 
specifications and in conformity with the plumbing regulations. 

3. To test the finished work and see that it is gas- and water- 
tight. 

Lead Pipes should be examined as delivered. The weight 
per foot, or the letter denoting the same thing, is stamped on 
the ends of the coils ; after the ends are cut off it is difficult to 
ascertain whether they comply with the requirements of the 
specification, for the saw used in cutting spreads out the lead, 
thus giving the enri an apparently greater thickness. Pipes 
showing unequal thickness of metal and those having a honey- 
combed appearance or in any way corroded should be rejected. 

Table 65. 

WEIGHT OF LEAD WASTE-PIPE, 

IJ in 2 lbs. per foot 

2 ** 3 and 4 lbs. per foot 

3 " 3| and 5 lbs. per foot 

3^ *' 4 lbs. per foot. 

4 *' 5, 6, and 8 lbs. per foot 

4^ ** , 6 and 8 lbs. per foot 

5 " 8, 10, and 12 lbs. per foot 



318 



PLUMBING. — INSPECTIOis^ OF PLUMBING. 



Table 66. 
WEIGHT AND THICKNESS OF LEAD PIPE. 



1 
6 




1 


o 

JO 

la 


J, 9 


ax 

U2 


1 




1 


i 




5r 


i 

! ius. 




lb. oz. 


ins. 


lbs. 


lbs. 


ius. 




lb. oz. 


ins. 


lbs. 


lbs. 


8 


AAA 


1 12 


0.18 


1968 


492 


1 


A 


4 


0.21 


857 


214 


3 

8 


AA 


1 5 


0.15 


1627 


406 


1 


B 


3 4 


0.17 


745 


186 


3 


A 


1 2 


0.13 


1381 


347 


1 


C 


2 8 


0.14 


562 


140 


i 


B 


1 


0.125 


1342 


335 


1 


D 


2 4 


0.125 


518 


1^9 


i 


C 


14 


0.11 


1187 


296 


1 


E 


2 


0.10 


475 


118 


f 


- 


10 


0.087 


1085 


271 


1 


- 


1 8 


0.09 


325 


81 


^s 


- 


91 


0.08 


775 


193 


11 


AAA 


6 12 


0.275 


962 


240 


i 


AAA 


3 


0.25 


1787 


446 


u 


AA 


5 12 


0.25 


823 


205 


i 


- 


2 8 


0.225 


1655 


413 


1-i 


A 


4 11 


0.21 


685 


171 


i 


AA 


2 


0.18 


1393 


3Je 


li 


B 


3 11 


0.17 


546 


136 


1 
it 


A 


1 10 


0.16 


1285 


321 


1-i 


C 


3 


0.135 


420 


105 


i 


B 


1 3 


0.125 


980 


245 


li 


D 


2 8 


0.125 


350 


87 


i 


C 


1 


0.10 


782 


195 


u 


- 


2 


0.095 


322 


80 


i 


D 


9 


0.065 


468 


117 


H 


AAA 


8 


0.29 


742 


1P5 


i 


- 


10 


0.07 


556 


139 


n 


AA 


7 


0.25 


700 


175 


i 


- 


12 


0.09 


625 


156 


14 


A 


6 4 


0.22 


628 


157 


■i 


AAA 


3 8 


0.23 


1548 


387 


li 


B 


5 


0.18 


506 


126 


t 


AA 


2 12 


0.21 


1380 


345 


n 


C 


4 4 


0.15 


430 


107 


1 


A 


2 8 


0.18 


1152 


288 


u 


D 


3 8 


0.14 


315 


78 


1 


B 


2 


0.16 


987 


246 


H 


- 


3 


0.12 


245 


61 


f 


C 


1 7 


0.117 


795 


198 


If 


B 


5 


- 


- 


116 


1 


D 


1 4 


0.10 


708 


177 


1^ 


C 


4 


- 


- 


93 


i 


AAA 


4 14 


0.29 


1462 


365 


n 


D 


3 10 


0.12d» 


318 


79 


i 


AA 


3 8 


0.225 


1225 


306 


2 


AAA 


10 11 


0.30 


611 


152 


^ 


A 


3 


0.19 


1072 


268 


2 


A A 


8 14 


0.25 


511 


127 


3 

4 


B 


2 3 


0.15 


865 


216 


2 


A 


7 


0.21 


405 


101 


? 


C 


1 12 


0.125 


782 


195 


2 


B 


6 


0.19 


360 


90 


i 


D 


1 3 


0.09 


505 


126 


2 


C 


5 


0.16 


260 


65 


1 


AAA 


6 


0.30 


1230 


307 


2 


D 


4 


0.09 


200 


50 


1 


AA 


4 8 


0.23 


910 


227 












i 



PLUMBING. — INSPECTION OF PLUMBING. 



319 






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330 PLUMBIi^^G.— INSPECTION OF PLUMBING. 

Table 68. 

WEIGHT OF BLOCK-TIN PIPE. 

I in 4i, 6i, and 8 ozs. per foot 

i " 6, 7i and 10'' '' *' 

I*' SandlO *' *' *' 

f *' 10audl2 '' *' '* 

1 " 15andl8 *' '* ** 

11 '' IJ and 14 lbs. ** '* 

14 " 2and2i *' '* ** 

2 " 24 and 3 '* '' '* 

Cast-iron Soil-pipes should be carefully examined for light 
weight and unequal thickness of metal; the poorer qualities are- 
gen erally much thinner on one side than the other. The making 
of the joints must be closely watched to see that an excess of 
oakum is not used, nor that such improper materials as cotton 
waste, paper, and shavings are used in place of the oakum; also 
to see that a sufficiency of lead is used and that the joint is prop- 
erly calked. Melted lead simply poured in will not make a tight 
joint, since on cooling the shrinkage draws it away from the iron, 
and it must be forced again into contact with the calking-iron, 
applied at every point of the circumference; the finished joint 
should show the marks of the tool all around. 

The practice of partly filling the hub with lead and afterwards 
filling it up with putty should not be permitted. Such joints 
may stand the test, but are not durable. 

Table 69. 

WEIGHT OF CAST-IRON SOIL-PIPE. 

(Extra heavy,) 

Average Weight 
Diameter. per Foot. 

Inches. Pounds. 

2 5^ 

3 9i 

4 13 

5 17 

6 20 

7 27 

8 33^ 

10 45 

12 54 



PLUMBING. — INSPECTION OF PLUMBING. 321 

All sizes made iu 5.ft. lengths except 12-m., which is 6 ft. The 
length does not include the hub. 



Testing Plumbing. 

Several methods are practised for testing the tightness of 
j)lumbing, namely, air-pressure, water- pressure, peppermint, and 
smoke tests. The work is usually subjected to two tests. The 
first is called the ** Roughing Test," and the second the "Final 
Test." 

The Water Test is the most satisfactory for the roughing 
test. It should be applied after the rough iron- and lead- work is 
in place, and just before setting the fixtures. The manner of 
applying it is as follows i 

The main pipe is plugged outside of the house-trap and the 
system of pipes filled until the water rises to the top of the high- 
est pipe. While the pipes are full of water all joints should be 
examined closely for leaks, and those showing signs of leaking 
at once calked. The pipes should also be closely examined for 
cracks, etc., and if any are found defective they should be 
marked for removal. 

Peppermint Test. — The oil of peppermint, on account of its 
powerful odor, is extensively employed for testing the tightness 
of plumbing. It is sold expressly for this purpose in hermeti- 
cally sealed vials containing two ounces. The method of using 
it is as follows : All the traps of the system are filled with water, 
the air- and ventilating-pipes are stopped up, the oil is poured 
into the main soil-pipe at its highest point. Usually this point is 
three or four feet above the roof. After the oil there is poured 
in a quart or more of boiling water, and the mouth of the pipe 
immediately stopped up. The peppermint is volatilized by the 
heat of the water, and the vapor, unable to escape, penetrates 
every part of the system. The pipes are then thoroughly 
examined The slightest odor of peppermint in the building 
indicates a defect either in a joint or in the pipe, which must be 
sought for and remedied. 

The man who carries and applies the peppermint should not 
be permitted to enter the house until the test is completed, as he 
is liable to carry with him some trace of the odor, which will 
make the test useless. If no leak has been detected the plumbing 
can be pronounced safe. 



322 PLUMBING. — INSPECTIOIsr OF PLUMBING. 

The Smoke Test is cousidered the best for the final test. It is 
applied by burniug cotton waste or paper saturated with turpen- 
tine or kerosene in a suitable apparatus placed at the mouth of 
the main outlet-pipe. Each joint should be closely inspected, 
and the slightest odor of the smoke is an indication that the joint 
is not tight. 

When air-pressure is used a pressure of 10 pounds per square 
inch is generally exacted. 

During the final test the places where leaks are most liable to . 
be found are at the back vent horns of porcelain fixtures, floor 
connections of water closets and coupling joints; these should be 
carefully examined, as in his hurry to finish the job the plumber 
may have forgotten to put in the washers. 

The tightness of the water-service pipes is tested by ahydrauHc 
test-pump under a pressure of about twice the pressure in the city 
supply-mains. 



PLASTERING. — DEFINITIOK OF PLASTERING. 323 



VIII. Plastering. 
Definition of Plastering, 

Plaster is the name given to the various compositions em- 
ployed for covering the interior walls and ceilings of buildings. 

The term stucco is applied to the mortar coverings placed on 
Iche exterior of walls to protect the materials of the walls from 
disintegration, also to secure a smooth finish for the purpose of 
imitating stone. 

The material most extensively employed for interior work is 
lime mixed witn sand, with or without the addition of hair or 
plaster of Paris. Many patented cements and plasters are now on 
the market. They are known by specific names, such as Keene's 
cement, Acme and Climax cement plaster, Windso7' cement, Rock- 
wall plaster, Adamant, etc. The three last named are mixed 
with the proper proportion of sand by the manufacturers, and 
only require to be "wet up" before using. They should be 
manipulated strictly in accordance with the directions furnished 
by the manufacturers. 

For exterior work Portland or Rusendale cement and sand are 
generally used. 

The operation of plastering comprises* 1st. The preparing of 
the groundwork, which is formed of either wooden lat/is, wire 
netting, perforated steel sheets, Jiollow brick, or the hare brick or 
stonewalls. 2d. The spreading and finishing ot the plaster. 

Plastering is divided into three classes, according to the man- 
ner in which it is executed, as one-coat, two-coat, and three-coat 
work. 

The cements or mortars employed for plastering are usually 
divided into three classes, known as coarse stuff, fine stuff, and 
-finishing. 



324 MATERIALS AND TERMS USED IN PLASTERING. 



Materials and Terms used in Plastering. 

Angle-bead : Vertical beads, generally of wood, fixed to the 
exterior angles of walls, flush with the intended surface of the 
plaster. 

Angle STAFF. — A strip of wood fixed to the vertical angle of 
a wall, flush with the plastering of the two planes. It is de- 
signed as a substitute for plastering in a situation so much ex- 
posed. A round staff is known as an angle-bead. 

Black Mortar is made by mixing anthracite (hard coal) coal 
dust with the lime, instead of sand. 

Brown Coat or Browning is the name given to the second 
coat in three-coat work. It is composed of the same ingredi- 
ents as the first or scratch coat, with the addition of more sand 
to make it poorer, and therefore less liable to crack. Its thick- 
ness varies from one quarter to three eighths of an inch. If 
the first coat has become too dry it must be moistened with 
water before applying the browning. 

On brick and stone walls the scratching is sometimes omit- 
ted, and the brown coat is applied directly to the surface of the 
wall, and of the proper thickness to receive the finishing coat. 

Coarse Stuff. — The material employed for the first coat. 
When lime is used as the cementing medium it consists of about 
one part of quicklime to four parts of sand and about two 
pounds of hair. The sand and lime are mixed in the same man- 
ner as mortar for brickwork. The hair is added by the use of 
a rake or hoe. When the patent plasters are used the coarse 
stuff is usually furnished ready prepared hy the manufacturers, 
and only requires to be mixed with water for use. 

Coat. — A layer of plastering. 

A scratch-coat is the first of three coats. 

One-coat work is plastering in one coat without finish. 

Two coat work is plastering in two coats. 

Screed-coat : A coat set even with the edges of the screeds. 

Floated coat : A first coat laid on with a float. 

Slippped coat is the smoothing off of a brown coat with a small 
quantity of lime putty. 

The term " slipped " is also applied to the operation of apply- 
ing the brown coat to the fiist coat without scralchiug , this 
operation is also called laid off work. 



MATERIALS AND TERMS USED IN PLASTERING. 325 

Cornice : Auy moulded projection which crowns or finishes 
the part to which it is affixed. 

Dots : Nails driven into a wall to a certain depth, so that their 
protrudiug heads form a gauge of depth in laying on a coat of 
plaster. 

Dubbing Out : Filling up with coarse stuff irregularities in 
the face of a wall previous to finishing it with finer plaster. 

Fine Stuff is made of pure lump lime slaked lo paste with a 
moderate quantity of water and afterwards diluted with water 
to the consistency of cream, then placed in barrels, where it is 
allowed to settle and stiffen by evaporation to the proper con- 
dition for working. 

Fine stuff is used for what is termed a ''slipped coat," and 
with the addition of a small quantity of white sand or plaster 
of Paris it is used for a finishing coat. 

Finishing Coat. — The third or last coat of plaster. 

First Coat. — The primary coat of coarse stuff. That of two- 
coat work is called laying when executed ou lath, and rendering 
when on brickwork. The first coat of three-coat work when ou 
lath is called the scratcJicodXy and when on brickwork rough 
ing in. 

Floated Lath and Plaster; Plastering of three coats, 
whereof the first is the scratch-coat, the second floating or floated 
work, and the last of fine stuff. 

Floated-work : Plastering rendered perfectly plane by 
means of a float. 

Floating-screeds : Strips of plaster previously set out on the 
work, at convenient intervals, for the range of the floating- rule 
or float. 

FuRRiNGS are strips of wood nailed to joists, rafters, or walls 
to bring their surf;ice to a level before nailing the plaster-laths. 

Gauge-stuff or Hard Finish is composed of fine stuff and 
plaster of Paris, in proportions regulated by the degree of rapidity 
required in hardening. As it sets rapidly, it should be prepared 
in small quantities at a time. It is used for the finishing coat of 
walls, for cornices, mouldings, and other kinds of orntvmenlation. 
The usual proportions are, for finishing, 3 to 4 volumes of putty 
to 1 volume of plaster of Paris, and for cornices, etc., about 
equal volumes of each. 

Hard finish is applied with the trowel, to the depth of about \ 
of an inch. It is polished with llie water-brush and trowel. 
Hard finish is also made wiii 1 part of fine stuff, 2 parts of 



32G MATERIALS AXD TEKMS USED li^ PLASTERING. 

white sand, and 1 part of marble-dust. When so composed 
it is called '* stucco.'' 

Grounds. — These are strips of wood sawed or planed carefully 
to a uniform thickness, three quarters of an inch or more where 
the plastering is to be three coat, or five eighths for two-coat 
work, secured to the furriugs in such a way us to give convenient 
nailings for the subsequent finishings, one row, for instance, 
being set an inch or so below the top of the future base-board, ' 
two or three in the height of a wainscoting, a border around 
each door and window, and so on. Being of equal thickness, 
and straightened with the straight-edge and plumb-rule to correct 
any irregularity in the furrings or studs, they afford guides for 
bringing the plaster to an even surface. 

Hair. — The hair used for plastering is obtained from the hides 
of cattle. It should be long, free from grease, dirt, and salt (hair 
from salted hides will make the walls damp) ; it should be well 
beaten, so as to straighten out the hairs, and then dried. The 
mixing of the hair and the mortar must be carefully done, so as 
not to break the hair into short bits. 

Hair is put up in paper bags, each bag beiug supposed to con- 
tain one bushel of hair when beaten up. It is sold by the bushel, 
which weighs from 14 to 15 pounds. It is classed according to 
quality as Nos. 1, 2, and 3, the last being the best. 

Jute is being used as a substitute for hair, and with satisfac- 
tory results. 

Hand-floating. — This is performed by using the float in the 
right hand, and a hair- brush holding water in the left ; both 
instruments are passed quickly over the wall at the same time, 
the brush preceding the float and wetting the surface to the re- 
quired degree. The firmness and tenacity of plastering are very 
considerably increased by hand-floating. The operation must 
take place while the mortar is green, when it is intended as a 
preparation for the setting coat. 

Hard Finish ; See Gauge-stuff. 

Keene*s Cement is a plaster produced by recalcining plaster 
of Paris after soaking it in a saturated solution of alum. It is 
made in two qualities, coarse and superfine. The latter is white 
and capable of receiving a high polish ; the former is not so 
white or able to take so good a polish, but sets hard. It is used 
for interior decorations, ariificial marbles, cornices, etc. 

Laid and Set : The terms used to describe two-coat plas- 
tering. 



MATERIALS AND TERMS USED IK PLASTERING. 327 

Laths, Wood. — Plasteriug-latbs are usually of mill-sawed 
white or yellow pine, spruce, or hemlock, in lengths of 4 feet, 
and are about IJ inches wide and J inch thick, and should be 
free from knots. 

They are nailed up horizontally to the studs and spaced | of 
an inch apart ; if placed nearer together the mortar will not be 
effectually pressed through the spaces, and its hold will be feeble; 
if farther apart it will not, while soft, sustain its own weight. 
Joints should be broken every course ; if the ends all joint on 
one stud the plaster will cruck at that point when the stud dries 
and shrinks. In placing laths above door- and window-heads 
they should extend at least to the next stud beyond the jamb, so 
as to prevent the radiating cracks which are apt to appear at that 
point. 

No deviation from the horizontal direction of the laths should 
be permitted, as cracks will show in the finished work where the 
change of direction was made. 

Laths are sold by the 1000 in bunches containing 100 laths. 

^. hundred square feet of plastering requires about 1400 laths. 

A lather will nail up from 10 to 20 bunches in a day. 

Laths, Metallic. — Metallic lathing is now made in a variety 
of forms, to meet the requirements of the different plastering 
compositions and the varying conditions of construction. 

In placing metallic lathings care is necessary to see that they 
are securely fastened and stretched, so that there may be no 
bulges or irregularities in the finished work. 

Lath-nails are from | to 1 inch long. To lath 100 square 
yards requires 10 pounds of 3d. nails. 

Laying : The first coat of plastering in two-coat work. 

Lime : The lime used in plastering should be the best quality 
wood-burned stone lime. 

Lime Moktar. — The mortar for plaster should be well made. 
The lime should be thoroughly slaked, and brought to a paste or 
putty state. It should remain in the mortar-bed until it is per- 
fectly cool. In this way only can the occurrence of particles of 
unslaked or partially slaked lime in the mortar be guarded 
against ; the presence of such particles in the finished work causes 
cracks and blisters by absorbing moisture. 

Authorities disagree as to the length of time the lime should be 
allowed to cool. The usual time is from six to fourteen days. 

Newly made mortar, if immediately applied, will chip, crack, 
and become mottled. 



328 MATERIALS AKD TEKMS USED IK PLASTEKIKG. 

In slaking the lime care must be taken that neither too much 
nor too little water is used. If too much is used the lime will be 
''chilled," and lose a part of its strength ; if too little it will 
"burn," and a portion of it will pass into the mortar-bed un- 
slaked and cause trouble there. 

Mixing the Mortar. — In regard to the manner of mixing the 
practice varies. 1st. The lime is slaked and when thoroughly 
cooled sufficient for the day's work is taken from the heap and 
mixed with the required proportions of sand and hair, then 
immediately spread upon the wall. The disadvantages of this 
process are the difficulty of distributing the hair evenly through 
the stiffened paste without the help of water to loosen the tufts, 
and the increased labor required to work the mortar. The advan- 
tages are the perfect hydration of the lime, by which chip-cracks 
and blisters are avoided ; the smoothness and hardness of the 
finished plastering, and its greater tenacity, since the hair not being 
added until the lime is cold retains its full strength instead of 
being burned and corroded by steeping in the hot caustic mix- 
ture, which is the first result of slaking. 2d. The lime is 
spread out, water poured on, and after a little stirring the hair is 
added and mixed with the steaming liquid. The sand is then 
added and mixed after which the mixture is piled for use. The 
hair in this method deteriorates as fast as the lime improves, and a 
season of cooling, which would be very beneficial to the latter 
ingredient, will nearly destroy the former, so that a course midway 
between the extremes should be taken. 

Lime Putty is lime dissolved in a small quantity of water, 
fresh lime being added from time to time, and the mixture stirred 
with a stick until the lime is entirely slaked, and the whole 
becomes of the consistence of cream ; it is next while still warm 
sifted or run through a hair sieve in order to separate the coarser 
parts of the lime, and is then ready for use. The material which 
remains in the sieve should be thrown away. 

Marble-dust is sometimes used for hard finishing. It should 
not be too fine, as it will then not make good work. If left 
about as coarse as sand it will be found to give the best satisfac- 
tion. 

When marble-dust is used it should not be mixed with the 
lime until a few moments before using, and no more should 
be prepared at one time than can be used up at once, as it " sets " 
quickly, after which it should not be used. 

The marble-dust must be prepared especially for plastering. 



MATERIALS AKD TERMS USED IK PLASTERING. 329 

and must not be the refuse from either grinding or sawing 
marble for commercial purposes, as such refuse contains particles 
of iron which will oxidize and show rust-spots in the finished 
plaster. 

One-coat Work : Plastering in one coat without finish. * 

Parge-work ; Pargetting : A particular sort of plaster- 
work, having patterns and ornaments raised upon it or indented. 

Pugging : Stuff laid between ceilings or on partition-walls to 
deaden sounds. 

Plaster of Paris is a white powder of sulphate of lime pro- 
duced by the gentle calcination of gypsum to a point short of 
the expulsion of the whole of the moisture. Paste made from it 
sets in a few minutes, and attains its full strength in an hour or 
two. At the time of setting it expands in volume, which makes 
it valuable for filling up holes and other defects in ordinary work. 
It is added to lime and other compositions in order to make them 
iiarden more rapidly. It is used for making all kinds of orna- 
inents for ceilings, cornices, angle-beads, etc. Some of these are 
cast by forcing it when in a pasty condition into moulds made of 
wax, plaster, etc. There are three qualities of plaster of Paris on 
the market — the superfine, fine, and coarse. 

It should be mixed by putting the powder into the water, not 
the water amongst the powder. 

Rendered and Set is complete two-coat work on brick or 
stone. 

Rendering : The first coat of plastering on brickwork. It is 
followed by the floating coat and the setting coat. 

Rough-cast : A mode of finishing outside work by dashing 
over the second coat of plaster while quite wet a layer of washed 
fine gravel or shells mln g with lime and water. 

Rule : A strip or screed of wood or plaster placed on the face 
of a wall as a guide to assist in keeping the plane surface. 

Sand for plaster should be angular, not too coarse nor too fine, 
and should be free from all foreign substances, particularly fine 
loam or clay. Clean river, or pit-sand, carefully screened, is 
generally considered the best for plaster. Sea-sand is deficient 
in sharpness and contains alkaline salts, which attract moisture, 
and is therefore unfit for use in plaster. Sand containing clay or 
loam may be cleansed by washing in a wooden trough having a 
current of water flowing through it ; when thoroughly cleaned it 
will leave no stain when rubbed between moist hands. Salts can 



330 MATERIALS AND TERMS USED IN PLASTERING. 

be detected by the taste, aud the size and sharpness can be 
judged by the eye or by the use of a microscope. 

Sand- FINISH has a rough surface resembling sandpaper ; it is 
composed of lime putty and coarse sand in equal proportions, 
and it is finished with a wooden or cork float. 

ScAGLioLA is composed of plaster of Paris with alum and some 
color mixed into a paste, and afterwards beaten on a prepared 
surface with fragments of marble. It is, when properly prepared, 
very hard aud susceptible of a fine polish. It is used in the for- 
mation of columns, walls, and ornamental work in imitation of 
marble. The surface on which it is to be placed has a rough 
coating of lime mortar with hair. 

When the composition has been laid on the prepared surface 
and is properly hardened the polishing is commenced by rub- 
bing the surface with pumice-stone and dampening it with a w^et 
sponge. It is next rubbed with tripoli and charcoal, and there- 
after with a felt rubber dipped in oil and tripoli, and finally 
finished off with felt or cotton dipped in oil only. 

Scratch-coat. — The first coat applied. It is intended to form 
a foundation for the succeeding coats. Its thickness varies from 
one quarter to three quarters of an inch. When lime is used 
it is composed of one part of quicklime to four parts of sand and 
about two pounds of hair to each bushel of lime ; this mixture is 
generally called coarse stuff. The operation of applying it to 
bare brick or stone walls is Xermii^ rendering, and when applied on 
laths laying. When completed and partially dry, though still 
quite soft, it is roughly scored or scratched (hence its name) 
with pointed sticks nearly through its thickness by lines run- 
ning diagonally across each other; these scorings are from two to 
four inches apart, and assist the adhesion of the succeeding coat. 

Before applying the scratch-coat to solid brick or stone walls 
tlie joints of the masonry should be raked out to a depth of at 
least one half inch the surface freed from dust and moistened 
with water. Old masonry if smoked or greasy should be also 
roughened. 

In applying to wood or metal laths the coarse stuff should be 
well tempered, and of such moderate consisteuc}^ that when 
pressed with force against the laths it will penetrate between 
them and bend down on the ii.side so as to form a good key. As 
this is the only way in which the whole body of the plaster can 
be kept on the walls, it is very essential that this work be well 
executed. Sometimes when plaster is applied to the surface of 



MATERIALS AND TERMS USED IN PLASTERING. 331 

brick or stone walls the scratch-coat is omitted and the brown 
coat applied directly of the required thickness to receive the 
finishing coat. 

Screeds are a kind of gauge or guide formed by applying to 
the first or scratch coat, when partly dried, vertical or horizontal 
strips of plastering-mortar, about eight inches wide and two to 
four feet apart, all around the room. These are made to project 
out from the first coat to the intended face of the second coat, 
and while soft are carefully made perfectly straight and out of 
wind with each other by means of the plumb-line, straight-edge, 
etc. When this is done the second coat is put on, filling up the 
horizontal spaces between them, and is readily brought to a 
perfectly flat surface corresponding to that of the screeds by 
means of long straight-edges extending over two or more of the 
screeds. 

ScREED-coAT AND Set are terms used also to designate two- 
coat work. The screeds are strips of mortar, six to eight inches 
in width and of the required thickness of the second coat, applied 
on the scratch-coat at the angles of the room, and parallel, at in- 
tervals of 8 to 5 feet, all over the surface to be covered. These 
screeds are carefully worked so as to be accurately in the same 
plane by the frequent application of the straight-edge in all 
possible directions. When they have become sufficiently hard to 
resist the pressure of the straight-edge the ''filling out'' of the 
interspaces flush with the surface of the screeds takes place, so as 
to produce a continuous, straight, and even surface. The surface 
is then hand-floated. 

Skim-coat is generally composed of lime putty and washed 
beach-sand in equal proportions. It is finished by trowelling over 
the surface from three to five times with a steel trowel and wet 
brush. 

Slipped-coat. — A slipped-coat is merely a smoothing off of a 
brown coat (coarse stuff) with the smallest quantity oi fine stuff 
or lime putty that will answer to secure a comparatively even 
surface. 

Stearate of Lime is composed of lime and beef suet. It is 
used as a finishing coat. The walls are prepared in the usual 
manner, with a scratch coat and a browning coat, the latter being 
" floated." When the browning is sufficiently dry the "stearate" 
is applied "hot " with an ordinary whitewash-brush. Two coats 
are generally applied. 

Stucco for interior work is composed of lime, putty, and white 



332 MATERIALS AND TERMS USED IN PLASTERING. 

sand. The usual proportious are three to four volumes of sand 
to one of putty (marble dust is sometimes added). It is applied 
with the trowel to the thickness of about one-eighth of an inch. 
It is well hand-floated, the water-brush being used freely while 
so doing. After the wooden float has been used it is gone over 
with the cork float in the same manner. The surface is polished 
w'ith the trowel and brush. 

Stucco (Common) consists of three parts clean sharp sand and 
one part of lime. 

Stucco (Bastard) consists of fine stuff and a small quantity 
of sand, and sometimes hair is added. 

Stucco (Trowelled) is composed of two-thirds fine stuff 
and one-third fine clean sand. It is used for surfaces intended to 
be painled 

Stucco —The name stucco is also given to the plastering on 
exterior walls. The materials used for this work are generally 
Portland or Rosendale cement and sand. The mortar made from 
either of these cements is applied in two coats, laid on in one 
operation. That for the first coat should be somewhat thinner 
than that for the second, in order that it may be pressed into 
thorough contact with the wall The second coat is applied 
upon the first, while the latter is yet soft. The two coats thus 
laid should form one compact coat of about one-half inch in 
thickness. The finished stucco should be kept shaded from the 
direct rays of the sun for some days, and be moistened from time 
to time. 

As a modification of the above process the first coat is some- 
times omitted, or rather replaced by a wash of thick cream of 
pure cement, applied with a stiff brush from time to time, just 
before the mortar is put on. If the brush work is faithfully 
done, and not allowed to dry before the surface receives the 
stucco, an intimate contact and firm adhesion are sure to result. 

A necessary precaution in this kind of work is to secure the 
services of a faithful workman — one who will not spare his 
strength, or lay on any of the mortar too loosely, or on too dry a 
surface ; otherwise there will be portions without adhesion that 
will be thrown off on the first occurrence of frost. 

After the stucco has been on for a few days the whole surface 
should be carefully sounded with a small iron instrument like a 
tack-hammer when all places destitute of adhesion will be readily 
detected by their hollow sound. From these the stucco should 



TOOLS USED IN PLASTERING. 333 

be carefully removed, the surface rougliened aud wetted, aud 
new mortar applied. 

Two-coat Work. — Plastering in two coats is done either in a 
laying coat and set, or in a screed-coat and set. The screed-coai is 
also called the floated coat. Laying the first coat in two-coat 
work is resorted to in common work instead of screeding, when 
the finished surface is not required to be exactly even to a straight 
edge. 

After the first coat, whether it be a laying coat or a screed-coat, 
has become partially dry so as to resist the pressure of the 
trowel, it is ready for the setting or finishing coat. This may be 
either in slipped work^ stucco, bastard stucco, or hard finish In all 
cases the surface to receive it must be roughened or scratched 
with a suitable tool, and if too dry must be moistened. 

Three-coat Work.— The first and second coat are termed 
respectively the scratch co2ii and brown coat, and the third coat is 
either hard-finish or stucco. 

White-coating generally means a composition of lime, putty, 
plaster of Paris, and marble dust or white sand. 

Tools Used in Plastering. 

Darby r A float-tool , it is either single or double, as may be 
required, the single being for one man to use, the double for 
two. The single one should be 4 feet 5 inches long and about 4 
inches wide, with a handle near one end, and a cleat near the 
other end running lengthwise of the blade. The long darbys 
have a handle on each end. 

Float ; A trowel used in spreading or floating the plaster on 
to a wall or other surface. 

The Long Float is of such a length as to require two men to use 
it. 

The Hand Float, made of pine, is used for finishing. 

The Quick Float is used in finishing mouldings, . 

The Angle Float is shaped to fit the angle formed by the walls. 

The Cork Float is used for the same purpose as the wooden 
float. 

Hawk : A square piece of board with a handle in the centre 
of one side ; it is used for holding aud conveying the mortar. 

Hod for carrying mortar is formed by two boards, eleven and 
twelve inches wide respectively, and eighteen inches long, the wide 
board being nailed on the edge of the uu: row one, making u right- 






334 



TOOLS USED IN PLASTERING. 



angled trough : one end is inclosed, and the end piece is rounded 
over the top : the boards forming the sides are rounded at the 
opening A handle about four feet long and two inches in di- 
ameter is fastened about two inches forward of the middle, nearer 
to the open end. and a piece of wood called a pad is fitted with a 
V groove on the angle just back of the handle. 

Mitring Hod is a tool one foot or more long, and about one- 
eighth of an inch thick, and three inches wide ; the longest edge 
is sharp, and one end is bevelled off to about thirty degrees. It 
is used for cleaning out quirks in mouldings, angles, and 
cornices. 

Mortar BEDS are made of rough plank, and should be 
strongly put together. 

Mortar-board is a board similar to a table top, and is about 
forty inches square. It is used for holding the mortar delivered 
from the hod. 

Mortar- BOX • See Slack-box. 

Moulds These are used for running cornices, and are infinite 
in shape and variety The reverse of the contour of the cornice 
is cut out of sheet copper or iron, and is firmly attached to a 
piece of wood which is also cut out the reverse shape of the 
intended moulding. 

Paddle : This is a piece of pine wood less than three inches 
wide, and six long, by one thick : it is made wedge-shaped on 
one end, the other end being rounded off for a handle. Its use is 
to carry stuff into angles when finishing. 

Pointer.— This is a trowel of nearly the same shape as a brick- 
layer's, but only about four inches long. It is used for mending 
broken or defective cornices, etc. 

Scratcher. — This is generally made of short pieces of pine 
two inches wide and one inch thick; five or seven of them are 
nailed to two cleats, and are placed about an inch apart. The 
centre one is left longer than the others, so as to form a handle. 
The ends opposite to the handle are cut off square and pointed. 
When completed it resembles a gridiron. Its use is to make 
grooves in the first coat to form a key for the second coat. 

Sieves of either hair or wire are used for straining through 
putty for finishing. 

Slack-box.— This is generally made of boards, eight or nine 
feet long and from two to four feet wide, and twelve or sixteen 
inches in depth. The bottom should be made as tight as rough 
boards will permit. 



MATERIALS REQUIRED FOR PLASTERING. 



335 



Stopping and Picking-out Tools, also called mitring tools, 
are made of fine steel plates, seven or eight inches long, and of 
various widths and shapes. They are used for modelling and for 
fiiiishing mitres and returns to cornices by hand where the 
moulds cannot work. 

Trowels are of several kinds: the one for ordinary use is 
formed of light steel four inches wide and about twelve inches 
long; this is the laying and smoothing tool. The gauging trowel 
is used for gauging fine stuff for courses, etc. ; it varies in size 
from three to seven inches in length, and in form resembles a 
bricklayer's trowel. 



Table 70. 

QUANTITY OF MATERIALS REQUIRED FOR PLASTERING. 



Materials. 


One-coat 
Work. 
Scratch- 
coat. 

Ys" Thick. 


Two-coat 

Work. 
%" Thick. 


Three-coat 

Work. 
y^" Thick. 


Hard Finish. 
Ys" Thick. 


Lime (unslaked) 


Per Sq. Yd. 
.15 CU ft 


Per Sq. Yd. 

.25 CU. ft. 
.38 " - 
.17 lb. 
2 gals. 


Per Sq. Yd. 
.83 CU. ft. 
.38 '' *^ 
.18 lb. 
2^ gals. 


Per Sq. Yd, 
10 CU. ft. 


Sand 


.23 " '* 

.lOlbo 
li gals. 




Hair 




Water 


IgaL 
08 CU. ft. 


Plaster of Paris 













Table 71. 

AREA COVERED WITH ONE CUBIC FOOT OF CEMENT AND SANL 



Materials. Cubic Feet. 


Thickness. Inches. 


y^ 


% 


1 


Cement 1 


Sq. Yds. 

^ 

4f 


Sq. Yds. 
3f 


Sq. Yds. 

If 
2i 


1, sand 1 


1, " 2 





For rubble or very rough brick walls the area in the above table will be 
decreased. 



Illllllllllllliliiiiiiiiiiiiii .mmiiiiiiiiiiiiiiiiiaaimi 



336 INSPECTION OF PLASTERING. 



Inspection of Plastering, 

MoRTAK. — It is not always easy to tell by the appearance of a 
heap of plastering-mortar whether the lime, sand, and hair are of 
good quality and in suitable proportions. If properly mixed, 
which will be shown by the absence of streaks in the mass, a 
small quantity should be taken up on a trowel. If it hangs down 
from the edge without dropping off the quantity of hair is suffi- 
cient. 

On drying a small quantity of the mortar an excess of sand 
will be shown by its being easily rubbed away with the fingers. 

The quality of the lime is best tested by observing the slaking. 
It should slake energetically and fall into a smooth paste without 
any refractory lumps or particles of " core." If such are found' 
all the packages of that brand should be rejected. 

During the application of the scratch coat on laths the opera 
tion should be closely watched to see that the workman exertf 
sufficient pressure to force the mortar through the openings and 
cause it to bend over and form a hook or key. It is necessar}' 
that ceiling-plaster should clinch well over every lath and wall- 
plaster over every second or third. The scratching should be 
thoroughly executed It affords the key for the second coat. The 
application of the second or l)rown coat should not be begun un- 
til the first coat is thoroughly dry. 

After the brown coat is dry the rule-joints at the angles should 
be first made, then screeds worked in between Thestiaightness 
and accuracy of corners and angles should be insisted upon, as 
the eye detects any irregularity in the angle between walls, or 
between the wall and ceiling, while inequalities of the interme- 
diate portions are not so noticeable. When the screeds have har- 
dened a little the space between them is filled in with " brown" 
mortar, which is easily made perfectly even by means of the 
straight-edge. 

Cornices should be run before the last coat of plaster is ap- 
plied. The angles should be as rough as possible, to give them 
sufficient " key. " If there is a large mass of mortar to be left in 
the angle nails should be driven to hold up the coarse mortar 
used for " dubbing out " the cornice before the finishing coat is 
applied. 

See that the laths are properly spaced and nailed and that the 
joints are properly broken. When wire lathing is used see that 



INSPECTIOl!^ OF PLASTEKING. 337 

it is securely fastened and well stretched, so that there may be no 
bulges or irregularities in the finished work. 

In applying plaster directly to the surface of brick or stone 
walls the joints should be raked out to a depth of at least half an 
inch, the surface cleaned of dust and then thoroughly wetted. 

Care is necessary to prevent the injury of plastering by freez- 
ing in winter or by too rapid drying in summer. From the latter 
cause the finished work near the windows is often found covered 
with a network of minute cracks, particularly on the side which 
the wind strikes, while a breeze barely at the freezing-point will 
cover the surface with radiating crystals, disintegrating it so that 
on thawing again the mortar will scale off in patches. The rem- 
edy for this is to keep all openings protected by temporary win- 
dows or screens, consisting of wooden frames covered with cot- 
ton cloth well fitted to the openings. These coverings should not 
be removed until the glazed sashes are ready to take their place, 
because by opening the windows while the plaster is green and 
admitting a draft those portions exposed to its action will dry so 
rapidly that it will crack, warp, and break bond. 

Plastering Tile Arches. — When it is intended to plaster 
the under side of tile arches the inspector should see that the 
smoke and soot from the boiler used for the hoisting-plant are 
not allowed to strike the arches, as neither can be removed, and 
they will stain the plaster. For the same reason he should see 
that only clean water is used for mixing the mortar >_ and that it 
is not allowed to flow over the arches. 

Plaster should not be applied to the arches until they are well 
dried out, otherwise stains are liable to appear which cannot be 
concealed even by oil-paint. 



■■■■■■■■■■■■■■■.■.■.»»■■■.■.■»■ 



338 GLASS. 



IX. Glass and Glazing, 



Glass. 



The defects of glass are very apparent, and consist of waves, 
air-bubbles, twists, sand-specks, blisters, and patches of color. 
The difference between first and second quality glass is very 
slight, and must be learned by observation. Double-thick glass 
shows unevenness of surface more plainly than single-thick. 

The tensile strength of common glass varies from 2000 pounds 
to 3000 pounds per square inch, and its crushing strength from 
6000 pounds to 10,000 pounds. 

Ordinary window-glass is sold by the box, whatever may be 
the size of the panes ; a box contains as nearly 50 square feet as 
the dimensions of the panes will allow. Panes of any size can be 
made to order. A great variety of sizes are usually kept in 
stock, ranging from 6 X 8 to 44 X 56 inches. 

Sheet Glass is of various qualities, weighing from 12 to 42 
ounces per square foot. 

Single thick Glass is about j^^th of an inch thick. 

Double THICK is about Jth inch thick. 

Plate Glass ranges in thickness from yV^Ii to -Jth of an inch. 

Polished Plate ranges from -f^ to i inch thick. 

Rough- CAST Plate, used for flooring, is usually 6 inches 
wide, 11 inches long, and from ^ to 1 inch thick. 

Crown Glass is made in single and extra thick. It is said to 
be more free from color than sheet glass, and it has a finer 
surface. 

French Polished Plate Glass is considered to be the 
highest grade of window-glass in the market. May be obtained 
in lights varying from a piece one inch square to a light 8 feet 
wide and 14 feet long. 

The weight averages 3i pounds per square foot. 



GLAZING. 



339 



Table 72. 
THICKNESS AND WEIGHT OF SHEET GLASS. 



No. 



12 
13 
15 
16 
17 
19 



Thickness. 
Inches. 



.059 
.063 
.071 

.077 
.083 
.091 



/eight per. 




Sq. Ft. 


No. 


Ounces. 




12 


21 


13 P 


24 


15 


26 


16 


32 


17 . 


36 


19 


42 



Thickness. 
Inches. 



.100 
.111 
.125 
.154 
.167 
.200 



Weight per 

Sq. Ft. 

Ounces. 



21 
24 
26 
32 
36 
42 



Table 73. 

THICKNESS AND WEIGHT OF SKYLIGHT-GLASS. 



Dimensions. 
Inches. 


Thickness. 
Inches. 


Weight pel- 
Sq. Lbs. 


12 X 48 
15 X 60 
20 X 10 
94 X 156 


A 


250 
350 
500 

700 



Glazing". 

Glass is secured in the sashes by triangular pieces of tin called 
sprigs and putty ; the panes of glass should be a little smaller 
than the sash in which they are to rest, so that the edges ot the 
glass nowhere actually touch the frame. 

A layer of putty is spread over the narrow part of the rebates, 
upon which the glass is firmly bedded — this is called the lack- 
putty ; as the glass is pressed upon it the superfluous putty is 
squeezed out round the edges of the panes and cut off. 

The glass is then front-puttied, the rebate is stopped, that is, 
filled in with putty to a triangular section. 

Care must be taken that the putty does not project beyond the 
front of the rebate so as to be seen from the inside of the 
window. 

Glazing in roofs is usually done without putty ; galvanizediron 
sashes are usually employed for this purpose. 

Large panes of plate glnss are not usually hnrk-putticd, rubber 
and leather are usually employed for heavy i)aiies. 



340 PAINTING. — MATEKiALS EMPLOYED FOK PAINT. 



X. Painting. 
Materials employed for Paint. 

A paint consists of a base (usually a metallic oxide), a veMcle, 
and a solv'ni. 

Bases are while lead, red lead, zinc white, oxide of iron, etc. 

Vehicles are water and drying-oils. 

Solvents are spirits of turpentiue. 

Driers are red lead, litharge, acetate of lead, sulphate of 
zinc, biuoxide of manganese, etc.; they are used to make the 
vehicle dry more rapidly. 

Stainers. — When the finished color is desired to be different 
from that of the base, coloring-pigments are used. They must be 
more or less finely ground, so as to be capable when mixed with 
the vehicle of being spread out in a thin layer or film over the 
surface to be painted. 

Bases. 

White Lead {hydrated carbonate of lead). — There are two 
methods of producing white-lead pigment. In the older or 
Dutch method thin sheets of lead are placed over pots containing 
a weak acetic acid, and the pots imbedded in fermenting tan- 
bark, the temperature of which varies from 140° to 150° F. The 
fumes from the acid convert the lead into the carbonate in a few 
weeks, which is removed and ground to a fine powder. 

In the more modern process oxide of lead {litharge) is mixed 
with water and about 1 per cent of neutral acetate of lead, and 
carbonic acid gas poured over it. In this manner the oxide 
is quickly converted into white lead, which does not require 
grinding. 

Pure white lead is a heavy powder, white when first made; if 
ex| osed in the air it soon becomes gray by the action of sulphu- 
retted hydrogen. 



PAINTIKG.— MATERIALS EMPLOYED FOR PAINT. 341 

It is insoluble iu water, effervesces with dilute hydrochloric 
acid, dissolving when heated, and is easily soluble in dilute nitric 
acid. 

When healed on a slip of glass it becomes yellow. 

Adulterations. — White lead is often mixed with sulphate of 
baryta, sulphate of lead, gypsum and oxide of zinc (it is claimed 
that these substances render it less liable to be blackened by the 
action of sulphuretted hydrogen), whiting or chalk, and other inert 
pigments. 

Sulphate of baryta, the most common adulterant, is a dense, 
heavy, white substance, very like white lead in appearance. It 
absorbs very little oil, and may frequently be detected by the 
gritty feeling it produces when the paint is rubbed between the 
finger and thumb. The presence of the other ingredients may be 
detected by the change in the specific gravity of the lead when 
dry, or by various methods of analysis. 

Tests for White Lead. — Dry lead ; digest a small quantity 
with nitric acid, in which it dissolves readily on boiling. When 
ground with oil, the oil should be burned off, and the residue 
treated with nitric acid; or the white lead ground with oil may 
be boiled for some little time with strong nitric acid, which 
destroys the oil, and dissolves the lead on the addition of water. 

If sulphate of baryta be present, being insoluble in the acid it 
remains behind, and can be collected on a filter, washed with hot 
distilled water, and weighed. 

Sublimed Lead {substitute for white lead) is obtained as a by- 
product in the smelting of non-argentiferous lead ores. It is pre- 
pared in special furnaces, in which the material is roasted, and is 
one of the products of sublimation and partial oxidation of 
galena ore with bituminous coal as a fuel. The ore is first smelted 
with raw coal and slacked lime iu a furnace, using an air-blast to 
obtain the required heat; the hotter the fire the more lead is vola- 
tilized and the more " fume " is produced. The products of this 
smelting are pig lead, pasty slags containing more or less lead, 
zinc, and other constituents of the ore, and the *'fume." The 
latter is drawn off by an exhaust fan through a settling-chamber 
to a bag-house, which contains a large number of woollen bags 
for filtering the fume out of the gases. This ** fume" is a lead- 
colored, impalpable powder known as "blue powder," and owes 
its color to the sulphide and carbonaceous matter in it. It is 
ignited and allowed to burn for several hours, which converts it 
into white, coherent crusls. These crusts, with oxidating ores 



ULlUAA^hU^^UU 



342 PAINTIis^G. — MATERIALS EMPLOYED FOK PAINT. 

and iiearlh-slags, are next charged into a special furnace with a 
very hot coke tire. Tlie products of this smelting are pig lead, 
slags poor enough in lead to be thrown away, and the "fume,'' 
which in this case is perfectly white and in a fine state of subdi- 
vision, suitable for a white pigment, and is sold as such either 
dry or ground in oil. It is known to the trade as Joplin lead 
from the place where it was first manufactured, Joplin, Mo. It is 
also known as Picher lead, from the name of the manufacturing 
company. 

Zinc White (oxide of zinc) is produced either by distilling 
metallic zinc in retorts under a current of air, or by a process 
similar in principle to that described under Sublimed Lead. 
Zinc white dissolves in hydrochloric acid. 

OxYSULPHiDE OF ZiNC, prepared by precipitating chloride 
or sulphide of zinc by means of a soluble sulphate of sodium, 
barium, or calcium, is used as the base of some patented paints. 

Red Lead {red oxide of lead or minium) is produced by raising 
the oxide of lead (known commercially as litharge or massicot) . 
obtained in the melting of argentiferous lead ores to a high tem- 
perature, short of fusion, during which it absorbs oxygen from 
the air and is converted into red lead. It is prepared in specially 
constructed furnaces, on the hearth of which the lead is melted 
and kept at a low red heat, and continually stirred to allow oxi- 
dation to occur. The massicot so formed during 24 hours of 
exposure to the heat is taken out, ground to a fine powder and 
washed, and again subjected in the same furnace for 48 hours to 
the same low red heat, until a sample taken out appears a dark 
red while hot and a bright red w^hen cooling. The furnace is 
then closed and left to cool slowly, a condition most essential to 
ihe success of the operation. 

There are other methods of preparing red lead, but the above 
iS the most important. 

The carbonate, of lead is also used instead of the oxide for con- 
version into red lead, but when the temperature is properly regu- 
lated another pigment is obtained, called orange lead. Red lead 
ihus produced retains a little carbonic acid and forms a pigment 
known as Paris red. 

Adulteration op Red Lead. — Commercial red lead con- 
tains all of the foreign metallic oxides — such as the oxides of 
silver, copper, and iron — with which the litharge used in pre- 
paring it is contaminated. It is also nduUerat(Ml wilh tlie red 
oxide of iron, boles, or brick-dust. These substances remain uu- 



PAINTING.— MATEBIALS EMPLOYED FOR PAINT. 343 

dissolved when the red lead is digested in warm dilate nitric 
acid; boiling hydrochloric acid extracts the sesquioxide of iron 
from the residue. When red lead thus adulterated is ignited 
there remains a mixture of yellow lead oxide and the red sub- 
stances that have been added to it. Brick-dust may be detected 
by heating the lead in a crucible and treating it with dilute nitric 
acid. The lead will be dissolved, but the brick-dust will remain. 

Antimony Yekmillion {sulphide of antimony), produced from 
antimony ore, is used as a substitute for red lead. 

Oxide of Iron is produced from the brown hematite ores. 
The ore is roasted, separated from impurities, and then ground. 
Tints varying from yellowish brown to black may be obtained 
by altering the temperature and other conditions under which it 
is roasted. It is also produced as a by-product in the manufac- 
ture of aniline dyes. 

Vehicles. 

Raw Linseed-oil is produced by compressing flaxseed. 
The oil as first expressed from the seed is allowed to settle until 
it can be drawn off clear. 

Raw linseed-oil, when of good quality, should be pale in color, 
perfectly transparent, almost free from odor, and sweet in taste. 
Darkness in color and slowness in drying indicate inferior quality. 
These defects are diminished and the quality of the oil improved 
by age. 

The oil should not be used within six months after being pro- 
duced ; it improves by keeping. 

Raw oil is more suited for delicate work than boiled oil, as it 
it is thinner, and lighter in color. When it is to be used for 
such purpose it is clarified by adding an acid (usually muriatic), 
which is afterwards carefully washed out. 

Raw oil spread in a thin film on glass or other n on -absorbent 
material will take from two to three days to dry, according to 
the state of the weather. 

The drying quality and the color of raw oil may be improved 
by adding about one pound of white lead to every gallon of oil 
and allowing it to settle for about a week. The oil is drawn off, 
and the lead can be used for painting rough work. 

Boiled Linseed-oil is prepared by heating raw oil either 
alone or with driers, such as red lead, litliarge, etc., or bypassing 
a current of ;iir through raw oil. 

Boiled oil is thiclfer and darker in color than raw oil. 



U^^AAAAri 



344 PAINTIKG. — MATERIALS EMPLOYED EOK PAINT. 

Good boiled oil spread in a thin film upon glass should dry in 
from 12 to 24 hours, according to the state of the weather. 

Raw oil is used for interior work and for grinding up colors. 
Boiled oil is used for exterior work and is not suited for grinding 
color. 

Adulteration and Substitutes.— Linseed-oil is subject to 
various adulterations, as by the addition of fish, hemp, cotton- 
seed, resin, and mineral oils. These adulterations are difiicult to 
detect ; they change the odor and specific gravity, and deterio- 
rate the drying quality. 

Raw oil treated with liquid japan drier is frequentl}^ sold as 
boiled oil. Such oil is said to be boiled through the ''bung- 
hole." 

As substitutes, fish-oil and cotton-seed oil treated with benzine 
are used ; also oils prepared by patented processes, as Lucal-oil, 
Sipes-oil, Japan-oil, etc. 



Tests for Linseed-oil. 

Color. — Straw yellow. 

Commercial Weight. — 7^ pounds to gallon. 

Boiling-point.— 130° C. (260° F.). 

Solidifies at. 27° C. (17° F.). 

Specific Gravity at 15° C. (60° F.) is 20° Baume (0.932). 

Usual adulterants are (1) fish-oil ; (2) petroleum (parafline- 
oil, etc.); (3) cotton-seed oil. 

(1) Shake equal parts of oil and strong nitric acid in a small 
white glass vial or test-tube and allow to stand 10 to 30 minutes. 





Upper Stratum. 


Lower Stratum. 


Pure linseed-oil. 


Muddy olive green, 

which gradually 
changes to brown. 


Almost colorless. 


Presence of 
fish-oil. 


Decided deep-red 
brown. 


Deep red or cherry 
color. 



Note. — If only a small proportion of fish-oil is present, the 
color of the lower stratum will gradully disappear until it be- 
comes colorless. 

(2) Shake the oil with concentrated solution of potasli or ^oda 



P.VlKTTiTG.— MATEKIALS EMPLOYED FOR PAINT. 344(^ 

containirig a l.ttle grain alcohol, and then add warm water and 
shake again. Allow to stand for half hour, and if any petroleum 
(parafflne-oil) is present, it will separate from the soap and float 
on top. 

(3) Put samples of oils in tubes and place them in a freezing 
mixture (2 parts ice or snow, 1 part salt). If the oils solidify at 
0° or — 10° to — 13° F., then cotton-seed oil is probably present. 
(Pure linseed-oil solidifies at — 17° F.) 

With Hydrometer. 

First test specific gravity of an oil you know to be pure ; then 
test the doubtful oil at the same temperature. 

Twenty-five per cent cotton seed oil makes a difference of 1° 
Baume less than pure linseed-oil at the same temperature. 

Ten per cent paratfine-oil, at the same temperature, ^ less. 

Twenty per cent paraffine-oil, at the same temperature, IT less. 

Solvents. 

Spirits of Turpentine is a volatile oil obtained by the dis- 
tillation of the turpentine obtained by tapping or boxing the yel- 
low-pine trees of the Southern States. The residuum left after 
distillation is called rosin to distinguish it from the finer resins 
used for varnish, etc. 

Good turpentine is colorless, and has a pleasant pungent odor ; 
adulterated or inferior qualities have a disagreeable odor. 

Turpentine is used in paints to make them work more smoothly, 
and as a solvent for resins and other substances. 

Good turpentine should have a very slight residue when evap- 
orated. When spread upon any surface in a thin layer it should 
dry in 24 hours, leaving a hard dry varnish. 

Turpentine is often adulterated with mineral oil. The pure 
turpentine loses bulk by evaporation, and gains weight upon e.:- 
posure to the air. Adulterated with mineral oils, the spirit evapo- 
rates, leaving the oil without any assistance in hardening. 

Benzine, naphtha, etc., are used as substitutes. 

Tests for Turpentine. 
Color. — Crystal clear and water white. 
Commercial Weight. — 7 pounds to gallon. 
Boilino-point.— 160° to 165° C. (820 to 340° F.\ 
Specific Gravity at 15° C. (59° F.) is 3!° ]^ainne (0.870). 



344i PAIKTIKG. — MATEKIALS EMPLOYED FOR PAIXT. 

Usual adulterants are (1) rosin oil ; (2) petroleum benzine 
(or naphtha) ; (3) headlight oil (150" test). 

RosiN-oiL, if present, will retard evaporation. Its presence 
in any considerable quantity may be detected by allowing the 
turps to evaporate from a small dish or open cup, when the 
adulterant will remain as a sticky resinous oil, with very char- 
acteristic resin odor if ignited. 

Benzine (or naphtha) shows itself generally by its character- 
istic odor and rapid evaporation. Test with the hydrometer. Five 
per cent of this adulterant will make a difference of 1^° Baume. 

Pure turps @ 15" C. (SO** F.) is 31° Baume. 

5^ benzine '' '' 32^ '' 

\m *' '' '' 34° 

25^ *' ** '* 38° 

Headlight Oil (Petroleum, Paraffine, Oils, etc.). — These 
adulterants retard evaporation and can usually be detected by 
the delicate '* bluish bloom" or smoky bluish-yellow cloud they 
impart to the turps. 

{a) To detect small quantities of the adulterants fill two white 
glass vials, bottles, or tumblers (the longer the better), one with 
pure turpentine, one with the doubtful article ; hold both over a 
piece of black paper and look directly down into the liquid ; three 
to five per cent of any petroleum will impart a decided hloom or 
cloud to the turps. 

(6) Test with hydrometer : five per cent of headlight oil will 
make a difference of V Baume. 

Pure turps 15° C. (59° F.) is 31° Baume. 

5^ headlight oil '' '* Slh" " 

10^ '* '' '' 32° 

25^ " ** '* 34° 

33i^ '* •* " 35$° " 

Stainers or Pigments. 

Blacks. — Lampblack is the soot produced by burning oil, 
resin, bituminous coal, resinous woods, coal-tar, or tallow. 

Vegetable Black is the name given to black obtained from 
burning oil. 

Ivory-black is obtained by calcining waste ivory in close ves- 
sels and then grinding. 



PAINTING. — MATERIALS EMPLOYED FOR PAINT. 345 

Bone-black is prepared from bones in a similar manner to 
ivory-black. 

Blues. — Prussian Blue is made by mixing prussiate of pot- 
ash with a salt of iron. The prussiate of potash is obtained by 
calcining and digesting old leather, blood, hoofs, or other animal 
matter with carbonate of potash and iron filings. 

Blue Lead is obtained by subliming lead as described under 
Sublimed White Lead. 

Cobalt Blue is an oxide of cobalt made by roasting cobalt 
ore. 

Blue Ochre is a natural-colored clay. Other blues are made 
from mixtures of soda, silica, alum, sulphur, copper, lime, etc. 

Browns generally owe their color to oxide of iron. 

Kaw Umber is a clay colored by oxide of iron. 

Burnt Umber is raw umber burnt to give it a darker color. 

Burnt SienNx^ is produced by burning raw sienna. 

Spanish Brown is a clay or ochre colored by iron. 

Greens may be made by mixing blue and yellow pigments, 
as Prussian blue, chromate of lead, and sulphate of baryta ; but 
such mixtures are less durable than those produced direct from 
copper, arsenic, etc. 

Greens known by various trade names are produced by treating 
the acetate or carbonate of copper with sal-ammoniac. Chalk, 
lead, and alum are sometimes added. 

Greens are also made from the arsenites of copper, and from co- 
balt and ferrous oxide of zinc. 

Reds. — Red Lead. For description, see page 342. 

Yermillion is a sulphide of mercury, found in a natural state 
ias cinnabar. 

Yermillion is adulterated with red lead brightened with cosine, 
and with logwood mixed with molasses. 

Yermillion is tested by heating in a test-tube. If genuine it 
should entirely volatilize. 

Artificial vermillion is made from a mixture of sulphur and 
mercury. 

German vermillion is the tersulphide of antimony, and is of an 
orange- red color. 

Indian Red is ground hematite ore. 

Chinese Red and Persian Red are chromates of lead pro- 
duced by boiling white lead with a solution of bichromate of 
potash. 

Yenbtian RBa> is obtained by heating sulphate of iron pro- 



346 PAINTING. — SPECIAL PAINTS 

duce(l as a waste product of tin and copper works. It is often 
adulterated by mixing sulphate of lime wiih it. 

Yellows. — Chrome Yellows are chromates of lead produced 
by inixing dilute solutions of acetate or nitrate of lead and bi- 
chromate of potash. 

Naples Yellow is a salt of lead and antimony. 

Yellow Ochre is a natural clay colored by oxide of iron. 

Other yellows are made from arsenic or oxychloride of lead. 

Raw Sienna is a clay stained with oxides of iron and manga- 
nese. 

Proportions of Ingredients. 

The proportions of the materials used in preparing paints vary 
greatly. They depend upon the material to be painted, being 
different for wood and iron; the kind of surface, whether porous 
or not, the porous requiring more oil; and the degree of exposure 
to which the paint is to be subjected. 

If the surface is subsequently lo be varnished, the paint must 
contain a minimum of oil. If the work is exposed to the sun, 
turpentine is necessary to prevent blistering. The proportions 
also depend upon the quality of the materials used. More oil and 
turpentine will combine wnth pure than wiih impure white lead. 
And the different coats of paint vary in composition: the first 
coat on new work requires more oil. Turpentine is necessary to 
cause adherence to old work. 

The quantity of paint required for a given surface may be ap- 
proximately ascertained by the following rule : 

Divide the square feet of surface to be painted by 200. The quo- 
tient is the number of gallons of liquid paint required for two coats. 

Divide the square feet of surface to be painted by 18. The quo- 
tient is the number of pounds of white lead required for three 
coats. 

Special Paints. 

Bituminous or Asphalt paints are prepared by dissolving 
bitumen in parafRne, petroleum, naphtha, and benzine. 

P. B. Paint is composed of asphaltum dissolved in bisulphide 
of carbon. 

Black Bridge Paint is composed of asphaltum, linseed-oil, 
turpentine, and kauri-gum. 

Coal-tar Paint is composed of coal-tar cither alone or mixed 
with lime or other inert pigment, and mixed with fish oi mineral 
oils. O^l-tar paint is frequently substituted for asphaltum paint. 



PAINTING —SPECIAL PAINTS. 347 

Graphite Paint is prepared by mixing graphite with boiled 
linseed-oil to which a small percentage of litharge, red lead, man- 
ganese, or other metallic salt has been added at the time of boil- 
ing. 

Prince's Metallic Paint is made from a blue magnetic iron 
ore, containing about 50 per cent of iron peroxide, 25 per cent 
limestone, and 25 per cent sulphur; it is mined in Carbon Co., 
Pa. The ore is broken into small pieces, roasted, and then 
ground. Durhig this process it loses one third of its weight by 
the volatilization of the sulphur and other constituents. The 
prepared pigment is said to contain 72 per cent of iron peroxide 
and 28 per cent of hydraulic cement. It is mixed with oil, and 
one color (brown) only is made, 

Lowe's Metallic Paint, manufactured at Chattanooga, 
Tenn., is made from red fossiliferous iron ore, mined at Atalla, 
Ala., and at Ooltewah, Tenn. An analysis of the paint shows its 
composition to be — 

Iron peroxide 78.87 

Alumina 3 . 29 

Silica 11-96 

Water 5.07 

Phosphoric acid, lime, manganese, etc 80 

The mineral is crushed, then spread on steam^pans and thor- 
oughly dried, passed through buhr mills, bolted, and finally re- 
ground. 

Rocky Mountain Vermillion is prepared from an ore found 
near Rawlins, Wyo. The mineral is a hydrated oxide of iron 
with a fine dark red color, and has the following composition : 

Iron peroxide .... 90 . 2 

Sulphur and lime 1.4 

Insoluble matter 7.2 

Water 1.2 

The Iron -clad Paint Co., of Cleveland, O., manufacture 
four varieties of mineral pigments. No. 1, called ** Rossie " red, is 
made from ore mined in Wayne Co., N. Y., and has the following 
composition : 

Iron peroxide 60.50 

Alumina 5 . 63 

Calcium carbonate 15.66 

Silica 18.00 

Moisture 33 



348 PAINTING. — VARNISH. 

No. 2, or '* light brown/' is prepared from an ore mined in the 
iron district of Lake Superior, Mich., and has the following com- 
position : 

Iron peroxide , . . 77.25 

Alumina 7.00 

Calcium carbonate 1 84 

Silica 13.84 

Loss 07 

No. 3, called "brown purple," is made from an ore coming 
from the Jackson Mine, Mich., and has the following composi- 
tion : 

Iron peroxide 93.68 

Alumina 3.06 

Silica 3.20 

Sulphur and loss 06 

No. 4, or ''brown," is also derived from ore mined in the Lake 
Superior district. 

Slate Paints. — The use of ground slate and similar materials 
mixed with white lead is quite common. The Indiana Paint and 
Roofing Co. and the Grafton Paint Co. manufacture a large 
amount of paint from refuse slate, mixed with other pigments 
and ground in oil. 

Silicate Paints, Asbestos Paints, etc., are made under 
patents, and their composition is not generally known. 

Varnish. 

Varnish is made by dissolving gum or resin in oil, turpentine, 
or alcohol. In the first case the oil dries, and in the others the 
turpentine or alcohol evaporates, leaving in either case a film of 
resin over the surface, smooth, solid, and transparent. The 
quality of the varnish is determined by the amount of gloss, and 
its permanence, durability on exposure to the weather, toughness 
and hardness of the coating, and rapidity of drying. 

Oil Varnishes. — The gums principally used in the preparation 
of oil varnishes are amber, anime, and copal. The first is hard, 
tough, and soluble with difticulty, and dries slowly. Anime 
dries quickly, is nearly as hard and insoluble as amber, but is 
deficient in toughness, is liable to crack, and turns dark on ex- 



PAINTING. — VARNISH. 349 

posiire to light and air. Copal is next in durability to amber, 
jiud the paler kinds when made into varnish become lighter on 
exposure ; it is more largely used than any other gum in prepar- 
ing oil varnishes, anime being frequently added to impart drying 
qualities. 

Linseed oil boiled with substances such as sulphate of lead, 
etc., for clarifying and imparting drying qualities, is the usual 
vehicle for oil varnishes ; spirits of turpentine is added to the 
mixture of oil and gum while still hot. 

Inferior oil varnishes are made from mixtures of anime, colo- 
phony, rosin, litharge, acetate of lead, sulphate of copper, linseed 
oil and turpentine. 

Common rosin dissolved with the assistance of heat in linseed 
oil or turpentine is frequently mixed with other varnishes to im- 
part brilliancy, but imless sparingly used renders them liable to 
crack; it is also used as a substitute for the finer varnishes. 

Spirit Varnishes are made by dissolving the softer gums, 
such as mastic, dammar, and common resin, in the best turpen- 
tine. They dry more rapidly, are lighter in color, but not so 
tough and durable as the oil varnishes. They are less costly. 

The still softer gums, such as lac (shellac), sandarach, etc., 
dissolved in alcohol dry quickly, are harder and more glossy 
than the turpentine varnishes, but are apt to crack and scale off, 
and will not stand exposure. 

Water Varnishes consist of lac dissolved in hot water, mixed 
with just as much ammonia, borax, potash, or soda as will dis- 
solve the lac. The solution makes a varnish which will just bear 
washing. The alkalies darken the color of the lac. 

Asphalt Varnish is generally made from those varieties of 
asphaltum which are free from any notable amount of mineral 
matter, such as glance-pitch and giisonite. It is a combination 
of asphaltum, turpentine, and boiled linseed-oil, combined in such 
proportions or with such additional ingredients as each manufac- 
turer has learned to be desirable, and which he retains as a trade 
secret. Three of asphaltum to four of boiled oil, with fifteen to 
eighteen parts of turpentine, is a common formula. 

Coal-tar mixed with mineral or fish oil and benzine is fre- 
quently substituted for asphalt varnish. 



350 PAINTI^^G.— ^IISCELLANEOUS. 



Miscellaneous. 

Japanning consists in applying successive coats of japan, i. e., 
ordinary lead paint ground in oil and mixed with copal or anime 
varnish. Each coat is dried in turn at the highest temperature it 
will bear without melting. The surface is treated with several 
coats of varnish. 

Stains are liquid preparations of different tints applied to the 
carefully prepared, smooth, unpainted surface of light-colored 
woo 1, such as white pine, in order to give it the appearance of 
more rare and highly colored woods. 

Whitewash is pure white lime mixed with water. It should be 
made of hot lime and applied promptly, as it then adheres better. 
It will not stand rain for any great length of time, and is easily 
rubbed off. To prevent cracking and cause the wash to harden, 
add to every half-bushel of lime 2 pounds sulphate of zinc and 1 
pound of common salt. 

To produce colors, add to each bushel of lime 4 to 6 pounds of 
ochre for cream color; 6 to 8 pounds amber , 2 pounds Indian- 
red, and 2 pounds of lampblack for fawn color; 6 to 8 pounds 
raw amber and 3 or 4 pounds lampblack for buff or stone color. 

Whiting is pure white chalk ground to powder and mixed with 
water and size (glue). It will not stand exposure to the weather. 
Proportions, 6 pounds whiting to one quart of strong glue. The 
whiting is first covered with cold water for six hours, then mixed 
with size, and left in a cold place until it turns to jelly. It can 
then be diluted with water and applied. 

Kalsomine is composed of glue, Paris white, and water, col- 
ored according to taste and laid on the walls with a brush. 

Putty is a composition of ground whiting and linseed-oil 
b?aten up into a tough and tenacious cement. 

It is used for securing glass in window-sash, and for filling 
(stopping) crevices and nail-holes in woodwork which is to be 
painted. 



PAINTING. — INSPECTION OF PAINTING. 351 

Inspection of Painting. 

Woodwork. — In painting wood the first operation is termed 
*' knotting," that is, covering knots, sap and pitch streaks with 
shellac dissolved in naphtha or other solvent. Knots and pitch 
streaks if not killed will cause yellow stains in the finished work. 
Bad knots should be cut out and a piece of sound wood set in 
their place. Red lead and glue are sometimes used for killing 
knots. Hot lime is also used; it is left on the knots for about 24 
hours, then scraped off, and the surface coated with shellac. 

After knotting, the priming coat is applied. This coat gener- 
ally contains a large proportion of red lead, which makes it set 
liarder, and gives it the pink color. 

The wood must be thoroughly dry, clean, and free from dust 
and dirt before applying the priming coat. 

The object of this coat is to fill the pores of the wood before 
applying the coloring coats, which otherwise would be absorbed 
by the wood and wasted. 

The priming coat is of the utmost importance, and should be 
very carefully applied. A poor priming coat under a good fin- 
ishing is sure to give unsatisfactory results; therefore inferior 
materials should not be used. 

After the priming coat is dry the puttying or stopping of cracks 
and nail-holes is done. For this purpose the nails are '' set in " to 
the depth of ^ inch or more. After stopping the surface should 
be rubbed down with sandpaper and well dusted. 

The colored and finishing coats are then laid on. Each coat 
should be thoroughly dry before the next is applied. 

Paint should be put on by strokes parallel with the grain of the 
wood; and long smooth pieces, such as window and door casings, 
should be finished by drawing the brush carefully along the 
whole length, so that there may be no breaks in the lines. The 
brush must be constantly at right angles to the surface being 
painted, only the ends of the hairs touching it; for only in this 
manner is the paint forced into the pores of the wood, and at the 
same time distributed equally. If the brush be held obliquely to 
the work, it will leave the paint in thick masses wherever it is 
first applied after being dipped for a fresh supply into the pot, 
and the surface will be daubed, but not painted. 

Plaster to be painted should be carefully laid, and its surface 
free from air-bubbles or flaws caused by the " blowing " of the 
lime. 



352 PAINTING. — INSPECTION OF PAINTING. 

Special care must be taken that both the plaster and the wall are 
perfectly diy before they are painted. The surface of the plas- 
ter should be thoroughly brushed to remove dust and loose parti- 
cles. 

The surface of plaster is primed with either two or three coats 
of linseed-oil, red-lead priming, or patent fillers, when the priming 
is thoroughly dry the colored or finishing coats are applied. 

Tin. — In painting tin all traces of oil, grease, and resin must be 
first removed, and if necessary to secure a clean surface it may 
be washed with benzine. 

Ironwork. — Before painting wrought iron or steel it is essen- 
tial that the surface be absolutely free from scale, grease, rust, 
and moisture. Scale is removed by brushing with stiff wire 
brushes, and the rust by scraping with steel scrapers, by a sand- 
blast, or by pickling in diluted acid which is washed off with 
water. 

Rust has the peculiar property of spreading, and extending from 
a centre, if there is the slightest chance to do so. Hence a small 
spot of rust on the metal may grow under the surface of the paint, 
and in time the paint will be flaked off and the metal exposed to 
the destroying action of oxygen in the presence of water. There- 
fore close scrutiny is necessary to see that all traces of rust are 
removed. 

Deep-seated rust- spots may be removed by applying heat from 
a painter's torch, which converts the rust into peroxide of iron, 
which is harmless and can be easily dusted off. 

The adherence of the paint will be increased if the metal is 
moderately heated before it is primed. 

Test for Water-proof Paint. — Take a small piece of iron 
and paint it thoroughly with the paint to be tested. After dry- 
ing place it on a glass plate and wet it with water. Then place 
a watch-crystal or bell glass over it, making the edges tight with 
gum or varnish. If the paint is pervious to water, the water will 
graduall}^ disappear, being decomposed by the iron, the oxygen 
uniting with the iron to form rust. If the paint is absolutely 
waterproof the water will remain in the chamber indefinitely. 

Yarnishing. — In using varnish great care should be taken to 
have everything quite clean, washing it if necessary. The cans 
should be kept corked, the brushes free from oil and dirt, and the 
work protected from dust or smoke. 

Yarnish should be applied in very thin coats, laid on in the 
direction of the fibres of the wood, and sparingly at the angles. 



PAI2ITTIKG. — INSPECTION^ OF PAINTING. 353 

Good varnish should dry so quickly as to be free from sticki- 
aess in one or two days. Its drying will be greatly facilitated by 
the influence of light, but dampness and draughts of cold air must 
be avoided. 

No second or subsequent coat of varnish should be applied 
until the last is permuuently hard ; otherwise the drying of the 
under coats will be stopped. 

Tlie time required for this depends not only upon the kind of 
varnish, but also upon the state ot* the atmosphere. 

Under ordinary circumstances spirit variiislics require from 
:!2 to 3 hours between every coat, turpentine varnishes require 6 
or 8 hours, and oil varnishes slill longer — sometimes as much as 
24 hours. 

Oil varnishes are easier to apply than spirit varnishes, in conse- 
quence of their not drying so quickly. 

The surface of natural wood which is to be varnished should 
be ''liliea " before the varnish is applied, to prevent it from being 
wasted by sinking into the pores of the wood. 

Fillers are usually made under patents, and their exact compo- 
sition is not known. Any gelatinous substance or glue may be 
used. Flour and starch mixed with water, benzine, or turpen- 
tine are frequently used ; but the use of these compositions 
should not be permitted, as they make the wood damp producing 
mildew, which prevents the varnish from adhering properly. 

Varnish applied to painted work is liable to crack if the oil in 
the paint is not good ; also. If there is much oil of any kind in the 
paint, the varnish hardens more quickly than the paint and forms 
a rigid skin over it, which cracks when the paint contracts. 

The more oil a varnish contains the less liable is it to crack. 
One pint of varnish will cover about 16 square yards with a 
single coat. 

Blistering, Peeling, and Cracking of paint are generally 
caused by the presence of moisture, or by not allowing sufficient 
time between coats for the paint to dry hard. 

Spotting, Streaking or Discoloration is generally due to 
sap or rosin in unseasoned wood. 

Chalking and Fading are caused by the irregular application 
of the paint, insufficiency of oil or use of adulterated oil. 



354 WATER-SUPPLY. — IKSPECTIOX ^F CAST^IROK PIPES. 



XI. Water-supply. 



Materials employed. 



The coDStruction of a water-supply system may include any 
one or all of the materials and methods of construction described 
in the precediug pages, and the duty of the inspector will be the 
same as there stated. 



Inspection of Cast-iron Pipes. 

The cast iron used for the manufacture of pipes is prepared as 
described under Cast Iron, page 94, and the pipes are cast ver- 
tical, for the reasons stated under Notes on Founding, page 96 et 
seq. 

The usual requirements for the pipe-metal are that it shall be 
of gray pig iron, tough, and of such density and texture as will 
permit of its beiug easily cut and drilled by hand. 

In the foundry inspection the inspector should supervise the 
preparation of the moulds, the pouring of the metal, the cutting, 
cleaning, coating, testing, and weighing of all the castings. 

After removal from the flasks the pipes should be cleansed, 
both inside and outside, without the use of acid or other liquid ; 
steel brushes are the best. Then each pipe should be examined 
for cold shorts, lumps, swells, scales, blisters, air- aud sand-holes, 
thickness, diameter, depth of hub, and straightness. Hubs should 
be closel}^ examined for honeycomb. Spigot-ends should be 
square and of correct size, so they will enter the hubs without 
chipping. 

Cast-iron pipe which appears to the eye to be sound and of 
proper form may have one or more of the following imperfec- 
tions : 

1. A poor quality of iron. 

2. Shrinkage in the metal, due either to improper moulding, 
varying thickness of the shell, or too rapid cooling of the metal. 

3. Want of uniformity in the thickness of the shell, which i.s 
usually due to want of care or skill in moulding. 



WATER-SUPPLY. — INSPECTION OF CAST-IRON PIPES. 355 

Poor iron may be guarded against by the frequent taking and 
testing of sample bars. These bars should be taken from every 
melt and subjected to a transverse test. The dimensions recom- 
mended for the test-bars are 26 inches long, 2 inches wide, and 1 
incli thick, to be loaded in the centre between supports 24 inches 
apart (narrow sides vertical); such bars should not break with a 
less load than 1900 pounds, and should show a deflection of not 
less than y^^ of an inch before breaking. Tensile tests should 
show from 18,000 to 20,000 pounds per square inch. 

Shrinkage strains can only be remedied by proper treatment 
from the time the iron enters the flask until it is coated and 
tested. 

Pipe should not be stripped and taken from the pit while show- 
ing color of heat, for the reason that when the pipe is exposed to 
a sudden chill from cold air the shrinkage of the outer surface 
will induce internal strains. Too great stress cannot be laid on 
this matter of cooling down. 

To discover inequality of thickness every pipe should be cali- 
pered. The ordinary method is to roll each pipe slowly, and 
those that do not roll uniformly are calipered. 

To insure that the spigots will fit the hubs wrought-iron 
templets are used for testing the hub and wrought-iron rings for 
testing the spigot-ends. 

Testing Quality of the Metal. — The toughness and elas- 
ticity of the pipe-metal may be tested by taking sample i-ings of, 
say, 1 inch in width and hanging them upon a blunt knife-edge, 
and then suspending weigiits from the lo^'er edge at a point 
opposite to their support, noting their deflections down lo the 
breaking-point ; also by letting similar rings fall from known 
heights upon solid anvils. For testing transverse strength the 
beam test is usually employed. 

Beam Test. — Test-bars 26 inches long, 2 inches thick, and 1 
inch wide are placed narrow edge vertical on supports 24 inches 
apart and loaded in the middle until broken. The breaking load 
for this size specimen is about 1900 pounds, and it should show a 
deflection before breaking of not less than -f^^ of an inch. 

The tenacity of the iron may be tested by submitting it to 
direct tensile strain in a testing-machine. 

Coating the Pipes. — After being inspected the pipes are 
coated with some preservative material. The coating known ns 
Dr. Angus Smith's is extensively employed. This coating is a 
varnish obtained by distilling coal-tar until the naphtha is entirely 



356 WATEK-SUPPLY. — IKSPEGTIOK OP CAST-IROK PIPES. 

removed and the material deodorized. The varnish is used 
either as it comes from the still or with the addition of 5 or 6 per 
cent of linseed-oil. 

To coat the pipes the varnish is carefully heated in a tank that 
is suitable to receive the pipes to be coated to a temperature of 
about 300° F., when the pipes are immersed in it and allowed to 
remain until they attain a temperature equal to that of the bath. 

Another method is to heat the pipes in a retort or oven to a 
temperature of about 300^ F., and then immerse them in the bath 
of varnish, which is maintained at a temperature of not less 
than 210° F. 

When linseed-oil is mixed with the pitch it has a tendency at 
high temperature to separate and float upon the pitch. An oil 
derived from coal-tar by distillation is more frequently substi- 
stituted for the linseed-oil in practice. When the pipe is removed 
from the bath the coating should fume freely and be set perfectly 
hard within one hour from the time of its removal, and should be 
free from blisters. 

The Barff process for preserving iron consists in converting 
its surfaces into the magnetic or black oxide of iron, which 
undergoes no change whatever in the presence of moisture and 
atmospheric oxygen. The pipes are placed in a suitable cham- 
ber or oven, and the temperature raised to about 500° F. ; steam 
is then admitted and continued from 5 to 7 hours, at the end of 
which time the oxidation is complete. 

AspJialtum is also used for coating cast-iron, wrought-iron, 
and steel pipes. The asphaltum used should be neither too brit- 
tle nor too oily. It is melted at the necessary temperature, about 
250° F., and the pipes dipped. As a test for the quality of the 
coating, when cold tap it lightly with a hammer; if it adheres like 
the coating of tin or galvanized iron it is good, but if it comes off 
in chips the asphaltum employed is too brittle. 

Hydraulic Proof of Pipes.— When the cast pipes have re- 
ceived their preservative coating they are placed in a hydraulic 
proving-prcss and tested by water-pressure to the required 
amount, usually 300 lbs. per sq. in.; and while under such press- 
ure they are smartly tapped all over the surface with a three- 
pound steel hammer, having a point similar to a pick, attached to 
a handle 16 inches long. Any failure shown under this test is a 
cause for rejection. 

The pipes which have passed the hydraulic test are weighed, 
and the weight paintedVith white paint on the inside of the hub. 



WATER-SUPPLY. — IN^SPECTTON OF CAST-IRON PIPES. 357 

Laying the Pipe. — The pipes are laid in trenches excavated to 
the required depth. At the joints the bottom of the trench is exca- 
vated to a sufficient depth to permit the calker to reach the bottom 
of the joint ; the trench at this point is also made a little wider to 
give room for making the joint. Small pipes should be solidly 
bedded on the bottom of the trench ; large pipes are generally 
laid in wooden cradles, two or three cradles to a length of pipe. 

Calking Joints. — To form the joints a gasket made from hemp 
yarn, oakum, or jute is used, twisted in the form of a rope. This 
rope should be cut into pieces long enough to go round the pipe 
and lap a little; it must be well rammed into the hub with a yarn- 
ing- iron. 

Before ramming the yarn in the joint it should be seen that the 
joint-room is even all round the spigot; if not so the yarner drives 
one or more cold-chisels into the narrow places so as to crowd the 
pipe into line. 

To guide the molten lead into a joint a '* roll " made of ground 
fire-clay with a yarn-rope centre is used, or a " jointer '' made of 
canvas or rubber faced with steel may be used instead. The roll 
or jointer is placed around the pipe close to the bell, bringing the 
two ends on top, and turning them out along the pipe, forming a 
space called the " pouring-hole." If the joint be wet or very cold 
it is advisable to pour in a little oil ; this prevents the lead from 
chilling too soon, and prevents the spattering of the lead into the 
face of the man pouring it. 

The lead should be the best quality of soft lead, free from 
scrap, heated sufficiently to run freely, care being taken not to 
overheat or burn it during the melting ; the furnace should be 
frequently moved, so that the hot lead need not be carried far 
enough to give it time to cool. 

After the joint is poured and seems full the roll is removed ; 
the joint is examined all around and especially on the bottom to 
make sure that it is well filled, if not the lead should be cut out 
and the joint re-poured. Small cavities are sometimes permitted 
to be filled with cold lead plugs. To put in a plug of cold lead 
a chisel should be driven into the lead in the joint to form a 
cavity into which the plug should be driven in the form of a 
wedge. A plug or band of cold lead should never be placed against 
a flat surface of lead. 

The calking is performed by first cutting off the lump of lead 
at the pouring-hole, and then driving the chisel lightly between 
the lead and the surface of the pipe all around. Then, commenc- 



358 WATER-SUPPLY. — IKSPECTIOK OF CAST-IKON" PIPES. 

ing at the bottom of the joint, the lead is *' set np " a little at a 
tiDie, using tirst the narrowest calking-iron next to the spigot, 
then one a size wider, and so on until one is reached which about 
tills the joint and leaves a smooth surface on the lead. In this 
way the lead is forced into the recess in the bell and is also 
thoroughly consolidated near to the spigot. 

If the joint was not run full, so that the lead drives away from 
the reach of the tools, the joint "must be run over again, and 
under no circumstances in a case like this should a cold lead plug 
be driven in. 

Tools used in Calking. —The tools used in calking are the 
'* yarniug-iron," having an edge about y^g by | inch ; a *' cold- 
chisel " to cut off the superfluous lead and to start up a tight 
joint; and from 4 to 10 ''sets" or calking-irons, varying from 
y\r to f inch by about f of an inch broad at the face. Some 
calkers prefer those with an offset, others those with a single 
bend. The hammer should weigh from H to 2^ or 3 lbs., and 
should not be over 10 inches in length over all. 

Testing the Pipe.— After the pipes are laid and the joints 
calked, and before the back-filling is commenced, they are 
tested under an hydraulic pressure from 25 to 50 per cent greater 
tlian that under which they are to be used. The purpose of 
this test is (1) to detect defective pipes, because in handling the 
pipe it is liable to receive blows which cause invisible fractures, 
which may become the source of extensive leaks in use, also in 
calking the hubs of the pipe may be fractured; and (2) to detect 
defective workmanship in calking the joints. 

The length of pipe tested at one time is usually the distance 
between stop- valves. The stop-valve acts as the closure for one 
end, the open end being closed with a blank flange tapped to re- 
ceive the nozzle of the hose and held in place by wrought-iron 
screw-clamps which grip the under side of the bell or hub. To 
provide against drawing of the joints a log of timber fitted with 
a jack-screw is placed with one end bearing against the centre 
of the flange, and tlie other end firmly wedged in the solid earth 
at the end of the trench. 

After the pipes are filled or charged with water an ordinary 
hand force-pump such as is used to test boilers is connected by a 
hose to the pipes and worked until the desired pressure is in- 
dicated on the gauge. The inspector then examines each pipe, 
carefully tapping with a light hammer at several points on the 
surface, and especially at the hubs. A fractured pipe will be 



WATER-SUPPLY. — INSPECTIOK OF CAST-IROK PIPES. 359 

readily detected by the sound emitted. Such defective pipes 
should be marked to be cut out and replaced by sound ones, after 
which the test is repeated. The pipes haviug been found sound, 
the joints next receive attention; all sweating and otherwise de- 
fective joints are to be immediately recalked. 

Care must be taken before applying the pressure that all the 
air has been exhausted from the pipe. 

Back-filling. — After the pipes are tested the back-filling is 
commenced. It must be carefully done, all stones being excluded 
from the layer next the pipe. The earth should be replaced in 
layers of about 12 inches in depth, and each layer tamped with a 
rammer weighing about 20 pounds. Surplus earth should be re- 
moved and the surface left neatly rounded with sufiicient material 
to allow for settlement. 

Thickness of Cast-iron Water-pipes. — There is no stand- 
ard thickness of cast-iron water-pipe, and the product from dif- 
ferent foundries show wide variation. The following table con- 
tains the dimensions and weights adopted by a representative 
foundry. 



360 WATER-SUPPLY. — IISrSPECTION OF CAST-IRON PIPES. 






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WATEK-SUPPLY. — IlSTSPECTIOlSr OF CAST-IKON PIPES. 361 





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362 WATER-SUPPLY. — INSPECTIOK OF CAST-IROK PIPES. 



Table 75. 

SIZE AND WEIGHT OF STANDARD SPECIALS (APPROXIMATE). 



Crosses. 


Tees. 


Tees. 


90° E bows. 


Reducers. 


Plugs. 


in. 


lbs. 


in. 


lbs. 


in. 


lbs. 


in. 


lbs. 


in. 


lbs. 


in. 


lbs. 


2 


40 


2 


28 


24x12 


1425 


2 


14 


3x2 


35 


2 


2 


3 


104 


3 


76 


24x8 


1375 


3 


34 


4x3 


42 


3 


5 


3x2 


90 


3x2 


76 


24x6 


1375 


4 


48 


4x2 


40 


4 


8 


4 


150 


4 


100 


30 


3025 


6 


110 


6x4 


95 


6 


12 


4x3 


114 


4x3 


90 


30x24 


2640 


8 


145 


6x3 


80 


8 


26 


4x2 


110 


4x2 


87 


30x20 


2200 


10 


225 


8x6 


126 


10 


46 


6 


200 


6 


150 


30x12 


2035 


12 


370 


8x4 


116 


12 


66 


6x4 


150 


6x4 


130 


30x10 


2050 


14 


450 


8x3 


116 


14 


70 


6x3 


150 


6x3 


125 


30x6 


1825 


16 


525 


10x8 


212 


16 


100 


8 


325 


6x2 


120 


36 


5140 


20 


900 


10x6 


150 


20 


150 


8x6 


265 


8 


266 


36x30 


4200 


24 


1400 


10x4 


128 


24 


185 


8x4 


265 


8x6 


252 


36x12 


4050 






12x10 


278 


30 


370 


8x3 


225 


8x4 


222 










12x8 


254 






10 


510 


8x3 


220 






12x6 


250 




10x8 


415 


10 


390 






12x4 


250 




10x6 
10x4 


388 
338 


10x8 
10x6 


330 
312 


45° Branch. 
Pipes. 


% or 45° 
Bends. 


14x12 
14x10 


475 
430 


Cap:. 


10x3 


350 
700 


10x4 
10x3 


292 
290 






14x8 
14x6 


340 

285 




12 














12x10 


650 


12 


565 


3 


90 


3 


30 


16x12 


475 


3 


15 


12x8 


615 


12x10 


510 


6x6x4 


145 


4 


65 


16x10 


435 


4 


25 


12x6 


540 


12x8 


492 


8 


300 


6 


85 


20x16 


690 


6 


60 


12x4 


525 


12x6 


484 


8x6 


290 


8 


160 


20x14 


575 


8 


75 


12x3 


495 


12x4 


460 


24 


2765 


10 


190 


20x12 


540 


10 


100 


14x10 


750 


14x12 


650 


24x24x20 


2145 


12 


290 


20x8 


300 


12 


120 


14x8 


635 
570 


14x10 
14x8 


650 
575 


30 
36 


4170 
10300 


16 
20 


510 
740 


24x20 
30x24 


745 
1305 






14x6 




16 


1025 


14x6 


545 






24 


1425 


30x18 


1385 




16x14 


1070 


14x4 


525 




30 


2000 


36x30 


1730 


Drip- 


16x12 


1025 


14x3 


490 


Sleeves. 










Doxes. 


16x10 


1010 


16 


790 










16x8 


825 
700 


16x14 
16x12 


850 
825 




1/16 or 221^° 






4 




16x6 






235 


16x4 


650 


16x10 


890 


2 


10 


Bends. 






8 


355 


20 


1790 


16x8 


755 


3 


20 








10 


760 


20x12 


1370 


16x6 


630 


4 


44 








20 








1420 


20x10 


1225 


16x4 


655 


6 


65 


6 
8 
10 


150 
155 
165 
260 
500 
1280 
1735 










5.0x8 


1000 


20 


1375 


8 


86 












20x6 


1000 


20x16 


1115 


10 


140 








20x4 


1000 


20x12 


1025 


12 


176 








24 


2190 


20x10 


1090 


14 


208 


12 








24x20 


2020 


20x8 


900 


16 


340 


16 
24 
30 








24x6 


1340 


20x6 


875 


20 


500 








30x20 


2635 


20x4 


845 


24 


710 








30x12 


2250 
1995 


21x10 
24 


1465 

1875 


30 
36 


965 












30x8 




1500 









WATER-SUPPLY. — INSPECTION OF CAST-IKON PIPES. 363 
Table 76. 

WEIGHT OF LEAD AND GASKET REQUIRED FOR EACH JOINT 
OF CAST-IRON PIPE (WATER). 



Diameter. 


Gasket. 


Lead. 


Diameter. 


Gasket. 


Lead. 


Inches. 


Lbs. 


Lbs. 


Inches. 


Lbs. 


Lbs. 


2 


0.050 


31 


18 


.75 


33 


3 


.075 


41 


20 


1.00 


37 


4 


,115 


8 


24 


1.25 


45 


6 


.175 


13 


30 


1.75 


60 


8 


.25 


16 


36 


2.50 


80 


10 


.30 


18 


40 


3.00 


95 


12 


.35 


22 


42 


4.00 


105 


14 


.42 


25 


48 


5.00 


145 


16 


.45 


29 


60 


7.00 


191 



As the diameter and depth of the hubs vary, the above weights 
are only approximate. 



Inspection of Steel Pipe. 

The plates used for pipe-making are usually of ** shell" steel, 
such as is used in boiler- work. They are subjected to the same 
scrutiny for surface imperfections and tests for strength as steel 
employed for boiler-making. 

The thickness should be ascertained by carefully calipering 
the edges and centre of each plate, and those falling below the 
tolerance allowed by the specifications rejected. 

The drifting test applied is that the plates must stand the 
punching and enlarging to one-third their original diameter of a 
row of holes f inch in diameter, pitched IJ inches between 
centres, and two diameters from the edge of the plate, without 
cracking. 

The plates must be sufficiently tough and pliable to allow cold- 
Scarfing to a fine edge at the laps without cracking, and to be 
rolled to the circle of the pipe without crackiug between rivet- 
holes and the edge of the plate. 

The shop-driven rivets are usually of steel, the field rivets of 
double-refined iron. 

The joints are made telescopic. 

The seams are bevelled and hammer-calked until watertight, 
without packing or plugs. 



364 WATER-SUPPLY. — INSPECTION OF STEEL PIPE. 

The finished pipe is scraped and thoroughly cleaned from 
scale, etc.; and inspected. 

The outlets are formed with flanged iron castings riveted to 
the pipe, lead gaskets being used to secure a water-tight joint 
when bolts are used to fasten them. 

The examination of the riveting should be performed as 
directed under Inspection of Rivets, page 194. 

Coating the Pipes. — The pipes are coated with coal-tar, 
asphaltum, or one of the many patented coatings, by Immersing 
them in a bath of suitable size and allowing them to remain long 
enough to attain the temperature of the coating mixture (usually 
250° F.). They are then withdrawn the coating allowed to 
stiffen for about 15 minutes, and then again immersed for a short 
time to thicken the coat. 

After the coating is satisfactorily finished the pipes are sub- 
jected to a hydraulic test of the required pressure. If any leaks 
show they are recalked, recoated, and retested until each section 
is water-light at the prescribed pressure, 

Asphalt and Coal-tar Coating= — This coating is composed 
of natural asphaltum and coal-tar in the proportion of about four of 
asphaltum to one of coal-tar. The asphaltum should be free from 
petroleum residuum, and the coal-tar should be deodorized and 
free from oily or greasy substances. The ingredients are placed 
in a tank of suitable size and boiled and stirred until fluid by 
the application of either direct or indirect heat ; the latter is 
preferable. 

Testing the Coating. — The fitness of the asphalt, asphalt 
and coal-tar, or patented coaling is tested by immersing in the 
boiling mass a piece of |-inch steel not less than 6 inches square, 
and allowing it to remain for 10 minutes ; it is then removed and 
immediately cooled in ice- water; it is then struck smartly with a 
light hammer : if the coating cracks it indicates that it is too 
brittle ; if it does not crack the specimen is subjected to a tem- 
perature of 100° F ; if it softens it is too soft. If the coating 
withstands all of these tests and adheres firmly to the steel 
surface it may be considered satisfactory; if not it must be suit- 
ably altered. 

The quality of the coating- varnish must be frequently tested, 
and fresh materials added from time to time to keep it of the 
proper consistency. 

Laying the Pipe. — The sections as they come from the shop 
are riveted in pairs on the banks of the trench, then rolled on to 



WATER-SUPPLY. — VALVES AND HYDRANTS. 3G5 

skids placed across the trench, and raised in slings by tripod der- 
ricks sufficiently to allow the removal of the skids. They are 
then lowered into the trench, pinched up, and bolted to the last 
section laid The rivets in the upper side of the joints are then 
driven from the outside, a man inside the pipe ''holding on.** 
The rivets in the lower sides and bottom of the joints are then 
driven by men inside the pipe working on their knees with short- 
handled hammers. 

At every other joint a l^-inch tapped hole is left in the top of 
tha pipe, or hand-hole castings are placed near the rivet line, 
through which the outside driven rivets are passed to the holder 
on the inside; when the joint is finished the hole is closed with a 
cast iron plug or plate. 

Pieces of heavy burlap are spread on and in the pipe for the 
men to walk and stand upon, and after everything else is com- 
pleted every bruised or scratched pait of the inner and outer 
pipe-surface is carefully coated with asphalt paint. 

The back-filling, etc,, is carried out in the same manner as 
previously described under Cast-iron Pipe, page 359. 



Valves and Hydrants. 

Valves are examined for quality of material and workman- 
ship. They are subjected to the required hydraulic pressure 
test, and while under pressure the bodies are tested with the 
hammer in the same manner as cast iron pipe. The spindles, 
stuffing-boxes, disks, and valves are examined for quality of 
metal and workmanship. 

Hydrants are examined for quality of material and work- 
manship. 

Setting Valves and Hydrants —Care must be taken to 
set valves and hydrants vertical ; before setting they should be 
carefully examined and all sand or dirt should be cleaned out, 
especially from around the valve-seats Hydrants should have 
gravel or Droken stone placed around them for 1 foot below 
their base to 1 foot above the drip. Valve-boxes should be 
placed at each valve and the earth well tamped around them. 



366 SEWERAGE. — MATERIALS EMPLOYED FOR SEWERS. 



XII. Sewerage. 
Materials employed for Sewers. 

The materials used in the construction of sewers are vitrified- 
clay pipe, cement-concrete pipe, brick, stone, concrete, timber, 
etc. The quality of the several materials should be the same 
as described in the preceding pages under Structural Materials. 

Vitrified Pipe is made from clay and salt glazed. The 
pipes are moulded by "machinery, dried, and placed in a close kiln 
and gradually subjected to an intense heat. 

Salt GLAZE. — When the temperature is sufficient coarse salt 
is thrown upon the fire in small quantities; a portion of the salt 
vaporizes, which vapor, combining with the silica in the clay, 
produces a soda-salt or glass, which is a glaze and forms part of 
the body of the pipe. 

Slip-glaze is considered to be inferior to salt-glaze. It is 
applied as follows : After the pipes are made and dried they arr^ 
dipped into a solution of argillaceous earth or aluminous cla^ 
mixed to about the consistency of cream. After dipping, the 
pipes are placed in the kiln and burned; the heat fuses the clay, 
thus producing a smooth glazed surface. The slip-glaze is apt 
to peel off when the pipe is subjected to the action of acids or 
frost. 

If the glaze can be picked off with a knife it is an indication 
that the pipes are made from a clay that would not stand the 
high temperature required for salt-glazing, and are therefore 
probably slip-glazrd. 

The vitrii.ed pipes should be examined (1) to see that they 
are straight and not warped out of line; (2) that the bore is 
uniform from end to end; (3) that they are sound; (4) that 
they are well burned and that the glaze is uniform on both the 
interior and exterior surfaces; (5) that the interior is free from 
lumps and blisters; (6) that the hub and body of the pipe are 
free from fire-checks, cracks, and flaws. 

Each pipe as it is passed to the pipe-layer should be closely 
examined to make sure that none which may have been injured 
since the formal examination are laid in the trench. 



SEWERAGE. — MATERIALS EMPLOYED FOR SEWERS. 367 

In laying the pipes the spigot-end of the pipe should be laid 
downhill. 

Pipes of Concrete should meet the same requirements as 
vitrified-clay pipes, and in addition they should be thoroughly 
seasoned, as green pipes are liable to collapse when the weight of 
the earth comes upon them. A well-seasoned, sound cement pipe 
when struck a smart blow with a light hammer emits a clear 
metallic sound. 

Tests for Pipe. — The tests applied to ascertain the fitness of 
pipes for sewers are (1) a test for permeability, (2) resistance to 
crushing: (3) ability to withstand the action of chemicals. 

The test for permeability is made by first drying the pipe till 
it ceases to lose weight, and then submerging it in water, allow- 
ing it to remain at least 24 hours under water, then removing it 
from the water, wiping dry, and reweighing. The amount of 
moisture absorbed ranges from to 7 per cent. 

The impermeability of a pipe may also be tested by closing one 
end of the pipe with some suitable substance, then reversing it 
and filling it with water. If the material is not perfectly imper- 
vious it will soon be detected by the sweating of the pipe, as it la 
termed, or the appearance of water oozing on the outside, to- 
gether with the loss of water from the interior of the pipe. 

The power to resist chemical action may be tested by pulveriz 
ing a piece of the pipe and boiling it in hydrochloric acid, wash 
ing on a filter, and noting loss of weight. 

To ascertain the resistance of the pipes to crushing they may 
be placed in a hydraulic press and pressure applied in the usual 
way. 

The capability to resist shocks may be ascertained by dropping 
a known weight from a given height, the percussive action be- 
ing equal to the velocity multiplied by the weight. If a weight 
of 14 lbs. be used and dropped from the following heights the 
percussive force will be as stated : 

4 inch fall = 64.65 lbs. 

5 <. .. ^ 72.47 '* 

6 " '' = 79.38 *' 
'7 " '* = 85.74 '' 

The record of this test would appear as follows : 

Kind of pipe Diameter Weight 

Number of pieces when broken 



368 INSPECTION OF SEWER CONSTRUCTION. 

Remarks : After blows with 4-mch fall pipe (perfect) 

(cracked) (broken). 

Man-holes are shafts of brick masonry built up from the sewer 
to the surface of the street, of sufficient size for the entrance of a 
man, for the purpose of inspection and cleansing. The usual form 
of man-hole is circular or elliptical at the base, and tapering up- 
wards to near the surface of the street, where it receives the cast- 
iron frame and cover. 

Lamp HOLES are small shafts, usually formed of lengths of 6- 
iuchpipe, built up vertically from the sewer to the surface of the 
street, and there covered with a cast-iron frame and cover. The 
purpose of lamp-holes is for the introduction of a lamp to illu- 
miuate the interior of the sewer for examination. 

Flush TANKS are chambers of brick masonry, furnished with 
siphons which automatically and periodically empty the chamber, 
and thus cause a sudden and copious dash of water to flow 
through the sewer and cleanse it. They are usually supplied 
with water from the street-mains through an ordinary service- 
pipe of small size, and the admission of the water is controlled by 
an ordinary lever-handle stop-cock. 

Inspection of Sewer Construction. 

The inspector should be constantly present and watchful. His 
first duty will be to inspect the quality and dimensions of the 
material furnished ; second, to see that the trenches are properly 
excavated, sheathed, and braced ; and third, to see that the sewer 
is properly built and to the grades and lines given by the en- 
gineer. 

Pipe Sewers.— Examine each pipe for size, thickness, depth 
of socket, shape, fire-cracks, and blisters ; for soundness, by 
testing each pipe by its ring immediately before lowering into the 
trench. A pipe that does not give a perfectly ringing sound 
when struck with a light hammer should be rejected. 

See that the pipe is laid true to grade and line, that each length 
is properly bedded. For this purpose a recess should be cut in 
the bottom of the trench to receive the socket of the pipe ; other- 
wise the pipes will be supported by the sockets only. 

That the spigot-end of each pipe is properly entered and sent 
home in the socket of the adjoining pipe. 

That the gasket of hemp or oakum is properly used. The 
socket should not be filled with it to the exclusion of the mortar. 



IKSPECTION" OF SEWER CONSTEUCTION. 369 

That the Y branches are laid accordiug to plau, and their 
ends, if not immediately connected, closed with a suitable stop- 
per. 

That the cement is properly mixed and the joints carefully 
filled with it all round the pipe. Examine the bottom of the 
joints to see that this is done; also see that mud is not used in 
place of cement. 

See that no mortar passes into the interior of the pipe. If it 
does the gaskets have not been properly packed. 

That man-hole foundations are firm and substantial ; that the 
junctions of lateral sewers in the man-holes are built in a smooth 
and workmanlike manner; the bottoms of the man-holes formed 
to the shape required by the plans ; the head of the pipes entering 
the walls are cut in good shape ; that the walls are carried up to 
the surface in a symmetrical and smooth manner; that the iron 
steps are built in as required; that the walls aie plastered as 
called for in the specifications. 

That the joints after being cemented are not disturbed until 
filled around and over and tamped. The back-filling should be 
carefully done. No stones should be used for filling within a 
foot of the pipe. That the filling is carefully placed in the 
trench — not thrown in violently — and tamped with suitable tamp- 
ers until the material fills the trench solidly. 

That the surface of the ground is left in good condition for 
travel. 

Brick Sewers. — Examine the bricks for quality; select the 
hardest and smoothest for invert nnd sides. 

Examine foundation and see that timber or other material is 
properly placed and secured. 

See that profiles and centres are properly set and of suflicieut 
strength. 

Examine quality of cement and sand; see that the mortar is 
properly mixed and of the required proportions. 

Have the bricks well wet in dry weather and not too wet in 
damp weather. 

Watch the masons to see that they lay each brick to line with 
a full mortar-bed and joint, and without unnecessary pounding 
or pushing after it is in place. 

See that the joints are of such thickness that a full number of 
courses of brick can be used without splitting a course. 

If plastering ihe exterior is rcquiied see ihnt it is properly 
executed and not injured during the back hlling. 



sro 



IKSPEOTIOK" OF SEWER CONSTRUCTION". 



That man-holes are formed and built symmetrically of the 
dimensions required, steps built in, and exterior plastered. 

That slants and junctions are properly located and well built 
in and exterior ends closed with stoppers. 

Interior of sewer cleaned of loose cement, brick-chips, and 
other rubbish. 

If water is met in the trench care must be used to keep it away 
from the brickwork until the cement is set. 

If the lower course of sheathing is to be withdrawn it should 
be drawn above the crown of the arch before filling in; if it is 
left to be drawn afterwards there is danger that a crack will be 
caused in the brickwork. 

Back-filling to be carefully done and thoroughly rammed, and 
surface left in good condition. 

Table 77. 

LENGTH OF SEWER-PIPE ONE BARREL OF CEMENT WILL LAY. 



Diameter of Pipe. 


Length. 


Diameter of Pipe. 


Length. 


Inches. 


Feet. 


Inches. 


Feet. 


6 


1200 


15 


190 


8 


666 


18 


130 


10 


426 


20 


106 


13 


300 


24 


74 



Table 78. 

WEIGHT OF SALT-GLAZED SEWER-PIPE. 



Diameter. 


Weight per Foot. 


Diameter. 


Weight per Foot. 


Inches. 


Pounds. 


Inches. 


Pounds. 


2 


5 


.15 


62 


3 


7 


16 


72 


4 


10 


18 


84 


5 


13 


20 


109 


6 


16 


21 


118 


8 


24 


22 


122 


9 


28 


24 


136 


10 


31 


27 


230 


12 


42 


30 


270 


14 


60 


36 


360 



PAVING. — GRANITE-BLOCK PAVING. 371 



XIII. PAVING. 

Materials employed. 

The materials used for pavements are stone in the form of 
blocks and broken fragments, wood in the form of blocks and 
plank, asphalt in two forms — sheet and block, and clay in the 
form of brick. 

The stones employed are granite, trap, sandstone, and lime- 
stone. 

Granite-block Paving. 

Manijfactut^e of Granite Paying-blocks. — The manu- 
facture of paving blocks varies in many details from the ordi- 
nary methods of granite-cutting. The high skill and fine 
workmanship of the stone-cutter are not needed, but a quickness 
in seeing and taking advantage of the directions of cleavage, as 
well as a deftness in handling the necessary tools, is requisite. 

The tools used for making the blocks are knapping-hammers, 
opening-hammers, reels, chisels, and, for the initial splits, drills, 
wedges, and half-rounds. When the block-maker quarries his own 
stock it is called ** motion-work," and the same process is used 
as in quarrying stone for other purposes, except that, as large 
blocks are not required, most of it can be done with ping and 
featlu r. Slabs, having been split out in the usual manner lo sizes 
that n\;iy be easily turned over and handled by one man, are sub- 
divided into pieces corresponding approximately to the dimen- 
sions of the required blocks. This is done by striking repeated 
blows upon the rock along the line of the desired break with knap- 
ping and opening-hammers. When a break is to be made crosswise 
the grain it is frequently necessary to chisel a light groove across 
the face, and commonly across the adjacent sides, to guide the 
fracture produced by striking on the opposite surface with tlie 
opening-hammer. Good splits can, however, be made along 
either the rift or grain by the skilful use of the opening-hammer 
alone. Blocks brok n out in the manner described are trimmed 



372 PAVING. — INSPECTION OF GRANITE-BLOCK PAVING. 

and finished with the reel, which is a hand-hammer having a 
long, flat steel head attached to a short handle. 

Inspection of Granite-block Paving. 

As soon as the blocks are brought upon the work they must 
be inspected (1) as to their quality, (2) character of the dress- 
ing, and (3) as to their dimensions. 

The requirements of the specifications under which the work is 
being executed must be the guide for the acceptance or rejection 
of the blocks. In general it may be said, Reject all stones which 
are easily chipped by a smart blow with a light hammer. Rough 
aud ill-shaped blocks should not be permitted in first-class work. 

When stone is brought from more than one quarry, that from 
each quarry should be piled and laid in separate sections of the 
work. 

In laying the blocks see that those for each course are selected 
with regard to uniformity of depth and width, and that the 
longitudinal joints are broken by a lap of at least two inches. 

The ramming of the blocks requii-es close watching to see that 
it is properly done, and that every block is brought to a solid 
bearing. 

The practice of the workmen is invariably to use the rammer so 
as to secure a fair surface without any regard to the bearing of 
the blocks. The result of such surfacing process is to produce 
an unsightly and uneven roadway when the pressure of traflic is 
brought upon it. The rammer should weigh not less than 50 
pounds and have a diameter of not less than 3 inches. 

When the joints are to be filled with paving-pitch the opera- 
tion must be closely scrutinized to see that the required quantity 
is poured into the joints, and neither spilled over the surface of 
the pavement nor removed unused. 



PAVIKG.— PAVING-PITCH. 373 



Paving^-pitch. 

The bituminous material employed for filling the joints in 
paving is the tar produced in the manufacture of gas, which, 
when redistilled, is called distillate, and is numbered 1, 2, 3, 4, 
etc., according to its density; it is used alone and in combination 
with asphaltum, creosote, etc. 

The formula for the bituminous joint-filling used in New York 
City is : 

Refined Trinidad asphaltum 20 parts 

No. 4 coal-tar distillate 100 *' 

Residuum of petroleum 3 ** 

The mode of applying the paving-pitch is as follows : 

After the blocks are rammed the joints are filled to a depth of 
about two inches with clean gravel heated to a temperature of 
about 250*^ Fahr. Then the hot pitch is poured in until it forms 
a layer of about an inch on top of the gravel, then more gravel is 
filled in to a depth of about two inches and more pitch poured in 
until it appears on top of the gravel, then gravel is filled in until 
it reaches to within half an inch of the top of the blocks; this 
remaining half inch is filled with pitch, and then fine gravel or 
sand is sprinkled over the joint. 

In some cases the joints are first filled with the heated gravel, 
then the cement poured in until the joints are filled flush with the 
top of the pavement. This method is open to objection, for if 
the gravel is not sufficiently hot the pitch will be chilled and will 
not flow to the bottom of the joint, but instead will form a thin 
crust near the surface, which, under the action of frost and the 
vibration of traffic, will be quickly cracked and broken up; the 
gravel will settle and the blocks will be jarred loose, and the 
surface of the pavement will become a series of ridges and hol- 
lows. 

In heating the pitch care must be exercised that it is not coked, 
in which condition it is brittle and useless. 

The gravel is heated either in revolving cylinders or in rect- 
angular iron pans supported on piles of stones with a fire under- 
neath. The same apparatus is employed for drying sand when 
it becomes necessary to remove moisture. 

Trap, sandstone, and limestone blocks are laid in the same man- 
ner as described above for granite blocks. 



374 PAVIKG. — ASPHALT PAVEMENTS. 

All the stoue-block pavements are laid either on a bed of clea 
sand or on a layer of concrete. 

Wood Pavements. 

Wood pavements are formed of either rectangular or cylindri- 
cal blocks of wood. The rectangular blocks are generally 3 
inches wide, 9 inches long, and 6 inches deep; the round blocks 
are commonly 6 inches in diameter and 6 inches long. 

The kinds of wood used are cedar, cypress, juniper, yellow 
pine, mesquite, and recently ^'arra^ from Australia and pyingado 
from India have been used. 

The wood is used in its natural condition or impregnated with 
creosote or other chemical preservative. 

The blocks of wood are laid either on the natural soil, on beds 
of sand and gravel, on a layer of broken stone, on a layer of con- 
crete, or sometimes on a double layer of plank, in the same man- 
ner as described under Granite Paving. The joints are filled either 
with sand or paving-pitch or Portland cement grout. 



Asphalt PavemeDts. 

AsPHALTTC Paving Materials.— All asphaltic or bituminous 
pavements are composed of two essential parts, namely, the 
cementing material (matrix) and the resisting material (aggre- 
gate). Each has a distinct function to perform: the first furnishes 
and preserves the coherency of the mass; the second resists the 
wear of the traffic. 

Two classes of asphaltic paving compounds are in use, namely, 
natural and artificial. The natural variety is composed of either 
limestone or sandstone naturally cemented by bitumen. To this 
class belong the bituminous limestones of Europe, Texas, Utah, 
etc., and the bituminous sandstones of California, Kentucky, 
Texas, Indian Territory, etc. The artificial consists of mixtures of 
asphaltic cement manufactured, as described on page 49 ^^ 56g. , 
with sand and stone-dust. To this class belong the pavements 
made from Trinidad, Bermudez, Cuban, and similar asphaltums. 
For the artificial variety most of the hard bitumens are, when 
properly prepared, equally suitable. For the aggregate the most 
suitable materials are stone-dust from ihe harder rocks, su h as 
granite, trai), etc., and sliarp angular s;ind. These materials 



PAVING. — ASPHALT PAVEMENTS. 375 

should be entirely free from loam and vcg table impurities. The 
strength aud euduriiig qualities of the mixture will depend upon 
the quality, strength, aud proportion of each ingredient, as well 
as upon the cohesion of the matrix and its adhesion to the aggre- 
gate. 

Bituminous Limestone consists of carbonate of lime natu- 
rally cemented with bitumen in proportiou^varying from 80 to 93 
per cent of carbonate of lime and from 7 to 20 per cent of bitu- 
men. Its color when freshly broken is a dark (almost black) 
chocolate-brown, the darker color being due to a larger percent- 
age of bitumen. At a temperature of from 55° to 70° F. the 
material is hard and sonorous aud breaks easily with an ii-regular 
fracture ; at temperatures between 70° and 140" F. it softens, 
passing with the rise in temperature through various degrees of 
plasticity, until, at between 140° and 160° F., it begins lo crum- 
ble, at 312° F. it commences to melt, and at 280° F. it is com- 
pletely disintegrated. Its specific gravity is about 2.235. 

Bituminous limestone is the material employed for paving pur- 
poses throughout Europe. It is obtained principally from deposits 
at Val-de-Travers, canton of Neufch^tel, Switzerland; at Seyssel, 
in the department of Ain, France; at Ragusa, Sicily; at Limmer, 
near Hanover; and at Vorwohle, Germany. 

Bituminous limestone is found in several parts of the United 
States. Two of these deposits are at present being worked, one 
in Texas, the material from whi.ch is called ''lithocarbon," and 
one on the Wasatch Indian Reservation. These deposits contain 
from 10 to 30 per cent of bitumen. 

The bituminous limestones which contain about 10 per cent of 
bitumen are used for paving in their natural condition, being 
simply reduced to powder, heated until thoroughly softened, 
then spread while hot upon the foundation, and tamped and 
rammed until compacted. 

Bituminous Sandstones are composed of sandstone rock im- 
pregnated with bitumen in amounts varying from a trace to 70 
per cent. They are found both in Europe and America. In 
Europe they are chiefly used for the production of pure bitumen, 
which is extracted by boiling or macerating them with water. In 
the United States extensive deposits are found in the Western 
States, and since 1880 they have been gradually coming into use 
as a paving material, and now upwards of a hundred aud fifty 
miles of streets in Western cities are paved with them. They are 
prepared for use asa paving material by crushing to powder, which 



^1f6 PAVING. — ASPHALT PAVEMEKTS. 

is heated to about 250° F. or until it becomes plastic, theu spread 
upon the street and compressed by rolling ; sometimes sand or 
gravel is added, and it is stated that a mixture of about 80 per 
cent of gravel makes a durable pavement. 

Trinidad Asphaltum. — The deposits of asphaltum in the isl- 
and of Trinidad, W.^ I., have been the main source of supply for 
the asphaltum used in street-paving in the United States. Three 
kinds are found there, which have been named, according to the 
source, lake-pitch, land- or overflow-pitcJi, and iron-pitch. The first 
and most valuable kind is obtained from the so-called Pitch Lake. 

The term land- or over flow -^^iich. is applied to the deposits of 
asphaltum found outside of the lake. These deposits form exten- 
sive beds of variable thickness, and are covered with from a few 
to several feet of earth ; they are considered by some authorities 
to be formed from pitch which has overflowed from the lake, by 
others to be of entirely different origin. The name cheese-pitch 
is given to such portions of the land-pitch as more nearly resem- 
ble that obtained from the lake. 

The term iron-pitch is used to designate large and isolated 
masses of extremely hard asphaltum found both within and with- 
out the borders of the lake. It is supposed to have been formed 
by the action of heat caused by forest fires which, sweeping over 
the softer pitch, removed its more volatile constituents. 

The name epuree is given to asphaltum refined on the island of 
Trinidad. The process is con'ducted in a very crude manner in 
large, open, cast-iron sugar-boilers. 

The Characteristics of Crude Trinidad Asphaltum, both 
lake and land, are as follows ; It is composed of bitumen mixed 
with fine sand, clay, and vegetable matter. Its specific gravity 
varies according to the impurities present, but is usually about 
1.28. Its color when freshly excavated is a brown, which changes 
to black on exposure to the atmosphere. When freshly broken 
it emits the usual bituminous odor. It is porous, containing gas- 
cavities, and in consistency it resembles cheese. If left long 
enough in the sun the surface will soften and melt and will 
finally flow into a more or less compact mass. The average com- 
position of both the land and lake varieties is shown by the fol- 
lowing analyses ; 



PAVING. — ASPHALT PAVEMENTS 



377 



AVERAGE COMPOSITION OF TRINIDAD ASPHALTUM. 



Constituents. 


Lake. 


Land. 


Hard. 


Soft. 


Water 


Per Cent. 

27.85 

26.38 

7.63 

38.14 


Per Cent. 

34.10 

25.05 

6.85 

34.50 


Per Cent. 
26 62 


Iiiorsranic matter 


27.57 


Organic non-bituminous matter... 
Bitumen . .1.. 


8.05 
37.76 








100.00 


100.00 


100.00 


When the analyses are calculated 
to a basis of dry substances the 
composition is: Inorganic matter 

Organic matter not bitumen 

Bitumen 


36.56 
10.57 
52.87 


38.00 

9.64 

52.36 


37.74 
10.68 
51.58 








100.00 


100.00 


100.00 


The substances volatilized in 10 
hours at 400° F 


3.66 
190° F. 
200° F. 


12.24 
170° F. 
185° F. 


86 to 1 37 


The substances soften at 


200° to 250° F. 


*' " flow at 


210° to 328° F. 







Refined Trinidad Asphaltum. — The crude aspbaltum is 
defined or purified by melting it in iron kettles or stills by the 
application of indirect heat. 

The operation of refining proceeds as follows : During the 
healing the water and lighter oils are evaporated, the asphaltum 
is liquefied, the vegetable matter rises to the surface and is 
skimmed off, the earthy and silicious matters settle to the bot- 
tom, and the liquid asphaltum is drawn off into old cement- or 
flour-barrels. 

When the asphaltum is refined without agitation the residue 
remaining in the still forms a considerable percentage of the 
crude material, frequently amounting to 12 per cent, and it was 
at one time considered that the greater the amount of this residue 
the better the quality of the refined asphaltum ; but since agita- 
tion has been adopted the greater part of the earthy and silicious 
matters is retained in suspension and it has come to be con- 
sidered just as desirable for a part of the surface mixture as the 
sand which is subsequently added. The refined asphaltum, if 
for local use, is generally converted into cement in the same still 
in which it was refined. 

Thk Chakacteristics of Refined Trinidad Asphaltum 
are as follows .- 

The color is black with a homogeneous appearance. At a tern- 



378 



PAVING. — ASPHALT PAVEMENTS. 



perature of about 70° F. it is very brittle and breaks wit!i a con- 
choidal fracture ; it burns witli a yellowisli-vvbiie flame, and in 
burning emits an empyreumatic odor, and possesses little cement?* 
tious quality ; to give it the required plasticity and tenacity it is 
mixed while liquid with from 16 to 21 pounds of residuum oil to 
100 pounds of asphaltum in the manner described on page 49 etseg. 
The product resulting from the combination is called asphalt 
paving cement ; its consistency should be such that, at a tem* 
perature of from 70° lo 80° F., it can be easily indented with 
the fingers and on slight warming be drawn out in strings or 
threads. 
AVERAGE COMPOSITION OF REFINED TRINIDAD ASPHALTUM. 



•specific gravity at 77° F. 



Bitumen 

Organic matter not bituminous, 
[norganic matter. 



Bitumen soluble in petroleum naphtha, 

Per cent of total bitumen soluble 

Softens at 

Flows at . * c , 




Bermudez Asphalt. — This is the name given to the asphaltum 
obtained from a lake or deposit situated in the State of Bermudez, 
Venezuela. The crude asphaltum is of the same variety as the 
Trinidad, namely, bitumen mixed with sand, clay, and vegetable 
matter ; its average specific gravity is 1.09, and its average com- 
position is as follows ! 

Per Cent. 

Bitumen 93. 54 

Mineral matter 2. 16 

Organic matter not bituminous 1.15 

Water 3.15 



100.00 



Petrolene 77.90 

Asphaltene 21.08 

lietioe 1.02 



100 00 



PAVING. — ASPHALT PAVEMENTS. 379 

The refining process is practically similar to that described 
jnder Trinidad Asplialtura, but is much more rapid, owing to the 
small amount of water and mineral matter present. In manu- 
facturing the cement it requires much less petroleum residuum 
than the Trinidad on account of the large amount of oil that 
it contains ; it melts at a lower temperature than the Trinidad, 
and the following are some of its characteristics : at 60° F. com- 
pressible ; at 70° F. viscous and malleable ; at 100° F. flowing, 
and can be stretched in hair-like threads ; at 189° F. melts , at 
400° F. gives no flash. 

California Asphaltum. — Asphaltum is produced in Cali- 
fornia by refining the bitumen from the extensive sandstone and 
other deposits which are found in various parts of the Slate. 
The characteristics of both the crude and refined asphaltum from 
some of the more important deposits are shown by the following 
analysis . 



Analysis of Asphaltum from Bakersfield, Cal. 

Crude. Refined. 

Specific gravity 1.132 1.240 

Softensat 180° F. 150° F. 

Flows at 220° F. 180° F. 

Inorganic matter 9.57 p. c. 9.77 p. c. 

Bitumen soluble in CS2 85.49 p. c. 90.16 p. c. 

Bitumen soluble in ether 69.98 p. c. 86.45 p. c. 

Percentage of total bitumen soluble in 

ether 81.85 p. e. 95.88 p. c. 



analysis of Asphaltum from Asphalto, Cal. 

Crude. Refined 

Moisture 6.51 p. c. 0.42 p. c. 

Bitumen soluble in chloroform 84.79 p. c. 93.27 p. c. 

Organic matter (not bitumen) trace 0.54 p. c. 

Inorganic matter consisting of infuso- 
rial earth with traces of iron 8.70 p. c. 5.77 p. c. 

Petrolene soluble in acetone 67.50 p. c. 71.27 p. c. 

Asphaltene insoluble in acetone 32.50 p. c. 28.73 p. c. 

Combined sulphur (chemically held in 

the bitumen) 0.73 p. c. 



380 PAVING. — ASPHALT PAVEMENTS. 



Analysis op Asphaltum from Santa Barbara Co., Cal. 

Crude. Refined. 

Specific gravity. ... 1.250 

Orgauic uoo-bituminous matter. 1.10 p. c. 

luorguuic matter consisting of finely 
divided quartz with oxide of iron 
and alumina 39.75 p. c. 

Bitumen soluble in CS2 59.15 p. c. 

Bitumen soluble in petroleum naphtha 

(petrolene) 42.50 p. c. 

Asphaltene 7.35 p. e. 



Analysis of Asphaltum from Kern Co., Cal. 

Bitumen soluble in CSa 78.90 p. c. 

Mineral subst;inces — sand, clay, and silica 9.40 p. c. 

Coky and volatile matter 4. 53 p. c. 

Water and loss 7.17 p. c. 



Analysis of Bituminous Sandstone from Ventura Co., 

Cal. 

Bitumen 24.00 p. c. 

Silica 64.00 p. c. 

Oxide of iron ^ 12 00 c 
Calcium carbonate \ ^' 

Cements for paving and other purposes are manufactured from 
the refined asphaltum described above by the admixture of 
maltha ; the two substances are combined at a very low temper- 
ature, the heat beiug applied indirectly, and the mixing is per- 
formed mechanically ; the degree of softness can be made to suit 
any requirement. 

Asphalt Mastic. — In Europe mastic is made from a mixture 
of bituminous limestone and refined asphaltum (usually Trini- 
dad). The bituminous limestone is reduced to powder and mixed 
with about 8 per cent of refined asphaltum, then melted and thor- 
oughly mixed. The hot composition is run into moulds of vari- 
ous shapes, usually round or hexagonal, and of such dimensions 



PAVING. — ASPHALT PAVEMENTS. 381 

as will give a cake or block weighing about 56 pouuds; these 
blocks usually have the name of the source or factory moulded 
on them. 

The mastic is prepared for use by breaking the cakes into small 
pieces, and heating it with the addition of about 5 per cent of re- 
fined asphaltum. The mass is constantly stirred, and, when soft, 
sand and fine gravel are added and thoroughly incorporated by 
stirring for about two hours at a temperature of about 300° F., 
when it is ready for use. 

Asphalt mastic is also prepared from bituminous sandstones 
and maltha or refined asphaltum, and from asphalt paving- 
cement. The principal use of mastic is for sidewalks and floors. 
In Europe it is called asphalte coule in distinction from the com- 
pressed bituminous limestone, which is called asphalte comprimS, 

Artificial Asphalt Pavements. — The pavements made 
from Trinidad, Bermudez, California, and similar asphaltums are 
composed of mechanical mixtures of asphaltic cement, sand, and 
stone-dust. 

The asphaltic cement is prepared in the manner described on 
page 49. Its consistency should be such that at a temperature of 
from 70° to 80° F. it can be easily indented with the finger-nail, 
and on being heated to about 90° F. can be drawn out in strings 
and threads. 

The sand should be equal in quality to that used for hydraulic 
cement mortar; it must be entirely free from clay, loam, and veg- 
etable impurities; its grains should be angular and range from 
coarse to fine. 

The stone-dust is used to aid in filling the voids in the sand and 
thus reduce the amount of cement. The amount used varies 
with the coarseness of the sand and the quality of the cement, 
and ranges from 5 to 15 per cent. (The voids in sand vary from 
.3 to .5 per cent.) 

As to the quality of the stone-dust, that from any durable stone 
is equally suitable. Limestone-dust was originally used, and has 
never been entirely discarded. 

The paving composition is prepared by heating the mixed sand 
and stone-dust and the asphalt cement separately to a tempera- 
ture of about 800° F. The heated ingredients are measured into 
a pug-mill and thoroughly incorporated. When this is accom- 
plished the mixture is ready for use. It is hauled to the street 
and spread with iron rakes to such depth as will give the re- 
quired thickness when compacted (the finished thickness varies 



382 PAYING.— ASPHALT PAVEMENTS. 

between 1^ and 2Mnches). The reduction of thickness by com' 
pression is generall}' about 40 per cent. 

The mixture is sometimes hiid in two layers. The first is called 
the ** binder"- or " cushion '*- coat, it contains from 2 to 5 per cent 
more cement than the surface-coat; its thickness is usually i inch. 
The object of the binder-course is to unite the surface mixture 
with the foundation, which it does through the larger percentage 
of cement th;it it contains, and which if put in the surface mix- 
ture would render it too soft. 

The paving composition is compressed by means of rollers and 
tamping-irons, the latter being heated in a fire contained in an 
iron basket mounted on wheels. These irons are used for tamp- 
ing such portions as are inaccessible to the roller, viz., gutters, 
and around man-hole heads, etc. 

Two rollers are sometimes employed : one, weighing 5 to 6 tons 
and of narrow tread, is used to give the first compression; and 
the other, weighing about 10 tons and of broad tread, is used for 
finishing. The amount of rolling varies; the average is about 
one hour per thousand square yards of surface. After the pri- 
mary compression natuial hydraulic or any impalpable mineral 
matter is sprinkled over the surface to prevent the adhesion of 
the material to the roller and to give the surface a more pleasing 
appearance. When the asphalt is laid up to the curb the surface 
of the portion forming the gutter is painted with a coat of hot 
cement. 

The concrete for the foundation is prepared in the manner 
described on page 224 et seq. The concrete must be thoroughly 
set and its surface dry before the asphalt is laid upon it; if not the 
water will be sucked up and converted into steam, with the result 
thut coherence of the asphaltic mixture is prevented, and, al- 
though its surface may be smooth, the mass is really honeycombed, 
and as soon as the pavement is subjected to the action of traffic 
the voids or fissures formed by the steam appear on the surface, 
and the whole pavement is quickly broken up. 

Although asphaltum is a bad conductor of heat, and the 
cement retains its plasticity for several hours, occasions may and 
do arise through which the composition before it is spread has 
cooled ; its condition when this happens is analogous to hydraulic 
cement which has taken a *'set," and the same rules which 
apply to hydraulic cement in this condition should be respected 
in regard to asphaltic cement. 

The proportions of the ingredients in the paving mixture are 



PAYIiTG. — BROKE]S^ -STONE PAVEMENTS. 383 

not constant, but vary with the climate of the place where the 
pavement is to be used, the character of the saud, and the amount 
and character of the traffic that will use the pavement.. The 
range in the proportions is as follows : 

Asphalt cement 12 to 15 per cent 

Sand 70to83 ** ** 

Stone-dust 5 to 15 '* ** 

A cubic yard of the prepared material weighs about 4500 
pounds and will lay the following amount of wearing-surface : 

2i inches thick 12 square yards 

2 '* " 18 ** 

11 •* '* *.... 27 *' 

f^ One ton of refined asphaltum makes about 2300 pounds of 
asphalt cement, equal to about 3.4 cubic yards of surface 
material. 

Broken-stone Pavements. 

Telford Pavement is constructed about as follows : The 
surfat^e of the roadbed is graded uniformly and compressed by 
rolling. On this is laid a course of large irregular- shaped stones 
about 8 inches thick The broadest suiface is placed on the 
earth-bed, and the wedge-shaped spaces between the stones are 
then filled with smaller pieces and chips of stone. The project- 
ing corners of the large stones are then broken off with hammers, 
and the course rolled or not with a steam-roller. On the surface 
of the large stones a layer of broken stone is spread, the binding 
added, sprinkled, and rolled ; in some cases a second and third 
course of broken stone is added, sprinkled, and rolled in the 
same manner as the first, A surface-coat of screenings com- 
pletes the work. 

Macadam Pavement is constructed in the same manner as 
the Telford, omitting the lower course of large stone, the total 
depth of the broken stone varying from 4 to 12 inches in thickness. 

Inspection of Telford and Macadam.— In the construc- 
tion of either Telford or Macadam pavement the points to be 
observed are : 1. The perfect consolidation of the earth-bed. 

2. In Telford base the proper binding of the foundation-course. 

3. Cleanliness of the stone; it must be free from clay and loam. 



384 PAVIKG. — BROKEN-STONE PAVEMENTS. 

4. Size of the stODe. A riug-gauge of the diameter of the largest 
stone should be provided, through which a stone should be 
frequently passed to test the size. This gauge is rarely furnished, 
the rule being used instead. Long flaky pieces, or "tailings," 
must be excluded; they will never compact, no matter how much 
they are rolled. 5. An excessive quantity of binding must not 
be used. The proportion should be about equal to the voids in 
the broken stone. By using a larger quantity than this the 
amount of rolling is lessened, but at the expense of durability. 
6. The use of a large quantity of water must be avoided. A 
large quantity expedites the rolling, but softens the foundation. 
The water should be applied by a sprinkler, and not be thrown 
on in quantity from the plain nozzle of a hose. 7. The amount 
of rolling varies extremely with circumstances — the class of 
material, the amount of binding and water used, the gradient, 
and the pressure of steam maintained. The only guide for its 
proper amount is that it must be continued until the stones cease 
to creep in front or sink under the rolls, and the surface has 
become smooth and firm. The surface of a well-constructed 
broken-stone road should, after being rolled, look almost like an 
encaustic pavement. 

The rolling should be done slowly, commencing at the sides 
and advancing to the centre. 

Voids in Broken Stone. — The proportion of voids in broken 
stone, gravel, and sand may be determined in either of the follow- 
ing ways: (1) Determine the specific gravity of the material and 
from that the weight of a unit of volume of the solid. Weigh a 
unit of volume of the loose material. The difference between 
the weights divided by the first gives the proportion of the voids. 
(2) Wet the loose material thoroughly, fill a vessel of known 
capacity with it, and then pour in all the water the vessel will 
contain. Measure the volume of water required and divide this 
by the volume of the vessel; the quotient represents the propor- 
tion of voids. 

To ascertain the Weight of a cubic yard of broken stone, mul- 
tiply the weight of a cubic yard of the given stone by the propor- 
tion of voids (usually one-half); the result will be the weight of a 
cubic 3^ard of the stone when broken. 

The AREA covered by a cubic yard of ordinary broken stone is 
about 32 square yards of surface. 

When the stone is rolled the primitive volume Is reduced by 
about one-fourth. 



PAVIKG. — BRICK PAVEMEKTS. 385 

To fiud the area covered by one cubic yard, divide 86 by the 
thickness of the layer in inches for unrolled stone; the quotient 
is the number of square yards that can be covered. When the 
stone is rolled divide 27 by the final thickness in inches; the 
quotient is the number of square yards. 



Brick Pavements. 

The qualities essential to a good paving-brick are the same as 
for any other paving material, viz., hardness, toughness, and 
ability to resist the disintegrating effects of water and frost. The 
required qualities are imparted to the brick by a process of an- 
nealing. The bricks are burned just to the point of fusion, then 
the heat gradually reduced until the kiln is cold. The clay em- 
ployed in the manufacture of paving-brick must be rich in silica, 
free from lime, and able to vrithstand without fusing a red heat 
for a sufficient length of time to render the bricks hard, homoge- 
neous, and impervious to water. 

The characteristics of hrick suitable for paving are : 

1. Not to be acted upon by acids. 

3. Not to absorb more than ^^ of its weight of water in 48 
hours' immersion. 

3. Not susceptible to polish. 

4. Rough to the touch, resembling tine sandpaper. 

5. To give a clear ringing sound when struck together. 

6. When broken to show a compact, uniform, close-grained 
structure, free from air-holes and pebbles. Marked laminations 
are fatal defects. 

7. Not to spall, chip, or scale when quickly struck on the 
edges. 

8. Hard, but not brittle. 

Tests for Paving - brick. — Paving - bricks are tested to 
ascertain 

1. Resistance to crushing. 

2. Resistance to cross-breaking. 

3. Resistance to abrasion or impact. 

4. Porosity or absorptive power. 

The first test is conducted in a suitable testing-machine. The 
second is made by setting the brick edgewise on rounded knife- 
edges 7 inches apart, and loading it at the centre on a rounded 
knife-edge with weights until it breaks. 



386 PAVnTG. — BRICK PAVEMENTS. 

The breaking weight per square inch or the resistance to cross- 
breaking is deduced by the formula 

in which B = modulus of rupture; 
W = breaking load; 
I = distance between supports; 
b = breadth; 
d = depth or width. 

The resistance to abrasion is usually made in a "rattler," such 
as is employed in foundries to clean small castings. In it are 
placed several bricks (usually 5), with a quantity (about 100 
pounds) of cast-iron scrap in pieces weighing about half a pound 
each. The rattler is revolved at from 15 to 25 revolutions per 
minute for 30 minutes. The bricks are then weighed, replaced, 
and the operation repeated for another 30 minutes, when they are 
again weighed and the loss calculated. 

The Absorption Test is made by drying the brick and 
weighing it, then soaking it in water for a given number of hours 
(from 5 to 24) and weighing again. The difference in the dry and 
wet weights should be small. Any brick absorbing more than 
one per cent of its weight in 24 hours is open to suspicion as be- 
ing liable to disintegration from frost. 

A rough test for a well-burnt paving-brick is to let it drop flat- 
wise from a height of 4 feet onto a second brick set edgewise. It 
should stand this test without breaking. 

Laying Paving-bricks. — The foundations employed for 
bricks are sand, sand and gravel, broken stone, and cement con- 
crete. The bricks are laid in a bed of sand spread upon the 
foundaiion, and screeded to a uniform depth, ranging from 1^ to 
3 inches. 

The bricks are usually laid on edge in straight courses across 
the street, with the length of the bricks at right angles to the axis 
of the street. Joints should be broken by a lap of at teast 3 
inches. None but whole bricks should be used, except in start- 
ing a course or making a closure. Before the closure is made 
each single course must be pressed as compactly together as pos- 
sible with an iron bar applied to the curb-end of the row, and 
then keyed in place with a close-fitting brick. After 25 or 30 
feet of the pavement is laid every part of it must be rammed 



PAVING. — ARTIFICIAL-STONE PAVEMENTS. 387 

■with a rammer weighing not less than 50 pounds, and tlie bricks 
which sink below the general level must be removed and re- 
placed by a brick of greater depth. After the ramming and 
rectification the joint filling is applied. It is either sand, cement 
grout, or paving-pitch. 

Properties of Pa vino-bricks. — Paving-bricks range in 
weight from 5^ to 7J pounds ; in specific gravity, from 1.91 to 
2.70 ; in resistance to crushing, from 7000 to 18,000 pounds per 
square inch ; in resistance to cross-breaking, R = 1400 to 2000 
pounds ; in absorption, from 0.15 to 3 per cent in 24 hours. 
The dimensions vary according to locality and the requirements 
of the specifications. The * 'standard " bricks are 2^x4x8 inches, 
requiring 58 bricks to the square yard, and weigh 7 pounds each ; 
"repressed," 2Jx4x8i, requiring 61 to the square yard, and 
weigh 6J pounds each; "Metropolitan," 3x4x9, requiring 45 
to the square yard, and weigh 9J pounds each. 

Artilicial-stone Pavements. 

Pavements formed of artificial stone or concretes composed of 
hydraulic cement, crushed stone, sand, and gravel, with some- 
times the addition of some indurating mineral substance, as 
baryta, litharge, etc., are extensively used for sidewalk and alley 
pavements; they are usually manufactured under a patent, either 
in place or in the form of blocks at a factory. Several varieties 
are in use, known by special names, as '' kosmocrete," "grano- 
lithic," "monolithic," *'ferrolithic," " metalilhic," etc. The 
process of manufacture is practically the same for all kinds, the 
difference being in the indurating material employed. 

The manner of laying is practically the same for all kinds. 
The area to be paved is excavated to a minimum depth of 8 
inches and to such greater depths as the nature of the ground 
may require to secure a solid foundation. The surface of the 
ground so exposed is well compacted by ramming, and a layer of 
gravel, ashes, clinkers, or broken stone is spread and thoroughly 
consolidated by ramming; on this foundation the concrete wear- 
ing-surface is placed, rammed, and floated. 

The principal precaution to be observed with good materials is 
that proper provision is made against the action of frost. This 
action is provided against by laying the concrete in blocks, form- 
ing rectangles, squares, or other forms having areas ranging from 
6 to 30 square feet, strips of wood being employed to form moulds 



388 fAYi^O.— CUHBSTOKES. 

in which the concrete is placed. After the concrete is set these 
strips are removed, leaving joints about half an inch in width 
between the blocks. Under some patents these joints are filled 
with cement, under others with tarred paper, etc. 



Flagging. 

The stones used for flagging are granite, limestone, and sand- 
stone (Hudson River bluestone is a sandstone). The inspection 
will comprise the quality of the stone, the dimensions, especially 
the thickness and the dressing of the joints; the edges should be 
dressed true to the square for the whole thickness of the stone, 
and not left feather-edge, as is very common. The laying should 
be carefully done on a bed of sand, gravel, or cinders, and the 
joints filled with cement mortar. 



Curbstones. 

Curbstones are employed for the outer side of footways to sus- 
tain the pavement and form the gutter. The upper inside edge 
is set flush with the footwalk pavement, and the upper surface is 
cut to a bevel so that the water can flow over them into the 
gutter. The materials employed are granite, sandstone, blue- 
stone, artificial stones, etc. 

The inspection includes an examination of the quality, dimen- 
sions, cutting, and setting. 

The setting requires to be carefully done, so that the stones 
shall stand to the true line and grade; the ramming and bedding 
must be faithfully performed or the stones will sink and turn 
slightly over. Curbstones carelessly set never present a pleasing 
appearance. 



CHAPTER IV. 
MISCELLANEOUS. 

; Weights and Measures. 

The origin of English measures is the grain of corn. Thirty- 
two grains of wheat, dried and gathered from tbe middle of the 
ear, weighed what was called 1 pennyweight ; 20 pennyweights 
were called 1 ounce, and 20 ounces 1 pound. Subsequently the 
pennyweight was divided into 24 grains. 

Troy weight was afterwards introduced by William the Con- 
queror, from Troyes, in France; but it gave dissatisfaction, as the 
troy pound did not weigh as much as the pound then in use; 
consequently a mean weight was established, making 16 ounces 
equal to 1 pound, and called avoirdupois. 

Three grains of barleycorn well dried, placed end to end, made 
an inch— the basis of length. The length of the arm of King 
Henry I. was made the length of the ulna, or ell, which answers 
to the modern yard. 

The standard measure of length of both Great Britain and the 
United States is, in theory, that of a pendulum vibrating seconds 
at the level of the sea, in the latitude of London, in a vacuum, 
with Fahrenheit's thermometer at 62°. The length of such a 
pendulum is supposed to be divided into 39.1393 equal parts 
called inches, and 36 of these inches were adopted as the standard 
yard of both countries. 

Troy Weight. 

24 grains = 1 pennyweight : dwt. 

20 pennyweights = 1 ounce = 480 grains. 
12 ounces = 1 pound = 240 dwt. = 5760 grains = 22.7944 

cubic inches of distilled water, barometer 

30 inches. 



390 WEIGHTS AKD MEASURES. 

Avoirdupois or Commercial Weight. 
27.34375 grains = 1 drachm. 
16 drachms = 1 ounce = 437.5 grains. 

16 ounces = 1 pound = 256 drachms = 7000 grains =27.7015 

cubic inches of distilled water, barometer 
30 inches. 
28 pounds = 1 quarter = 448 ounces. 

4 quarters = 1 cwt. =112 pounds. 
20 cwt. = 1 ton = 80 quarters = 2240 pounds. 

The ton of 2240 pounds, known as the long ton, is the standard 
used by the United States Government at the customhouses, but 
in commercial transactions the short ton of 2000 pounds is used 
unless otherwise specified. 

Apothecaries' Weight. 
20 grains = 1 scruple. I 8 drachms = 1 ounce. 
3 scruples = 1 drachm. I 12 ounces = 1 pound. 
The grain in each of the foregoing tables is the same. 
An avoirdupois pound of pure water has the following 
volumes : 

At 32° F. = .016021 cubic feet or 27.684 cubic inches. 
39.1°'* =.016019 " *' "27.680 *' 
62^^ ♦' = .016037 " " '* 27.713 " 
212° *' = .016770 *' *' " 28.978 " ** 

Lineal Measure. 
12 inches = 1 foot. 
3 feet = 1 yard. 

5i yards = 1 rod or perch = 16J feet. 
40 rods = 1 furlong = 220 yards = 660 feet. 
8 furlongs = 1 mile = 320 rods = 1760 yards = 5280 feet. 
The British measure of length is about ^^ of an inch in 100 
feet, or 3f inches in a mile, shorter than that of the United States. 
To convert British linear dimensions into American multiply 
by 1.000058, and American into British multiply by .999942. 

Square Measure. 
144 square inches = 1 square foot. 
9 square feet = 1 square yard. 
30i square yards = 1 square rod. 
40 square rods = 1 rood. 
4 roods = 1 acre = 43560 square feet. 



WEIGHTS AND MEASURES. 391 

A square acre is 208.71 feet on each side. 
A circular acre is 235.504 feet in diameter. 
A half acre is = to 147.581 feet on each side. 
A quarter acre is = to 104.355 feet on each side. 
100 square feet = 1 square. 

Cubic or Solid Measure. 

1728 cubic inches = 1 cubic foot. 

27 cubic feet = 1 cubic yard. 

A perch of stone = 24. 75 cubic feet = 16' 6'' X 1' 6" X 1'. 

A cord of stone = 99 cubic feet = 4 perches. 

A cord of wood = 128 cubic feet = 4' X 4' X 8'. 

A ton of bituminous coal = 44 to 48 cubic feet. 
A ton of anthracite ** = 41 to 43 ** ** 

1 gallon water = 231 cubic inches. 

1 cubic foot = 7.48 gallons. 



Liquid Measure!. 

4 gills = 1 pint = 28.875 cubic inches. 
2 pints = 1 quart = 57.750 
4 quarts = 1 gallon = 231.0 
A cylinder 3i inches in diameter and 6 inches high will hold 
almost exactly 1 quart, and one 7 inches in diameter and 6 inches 
high will hold very nearly one gallon. 
A gallon of water weighs 8.338 pounds avoirdupois. 

Dry Measure. 

2 pints =1 quart = 1.16365 liquid quarts. 

4 quarts = 1 gallon = 268.8025 cubic inches. 

2 gallons =r 1 peck = 537.6050 '* 

4 pecks = 1 struck bushel = 2150.42 ** " 
A struck bushel = 1.24445 cubic feet. 
A cubic foot = .80356 of a struck bushel. 
A flour barrel contains 3 struck bushels. 

A heaped bushel = 1^ *' struck" bushels = 1.555 cubic feet. 
When heaped the cone must be at least 6 inches high. The 
bushel measure is a cylindrical vessel 18j inches in diameter and 
8 inches deep. 



392 WEIGHTS AND MEASURES. 

Miscellaneous Measures. 

12 units = 1 dozen. 

12 dozen = 1 gross. 

12 gross = 1 great gross. 

20 units = 1 score. 

24 sheets of paper = 1 quire. 
20 quires = 1 ream. 

2 reams = 1 bundle. 

5 bundles = 1 bale. 

25 lbs. powder = 1 keg. 
14 lbs. = 1 stone. 

100 lbs. = 1 quintal. 

1 chaldron = 36 bushels or 57.244 cubic feet. 

1 ton displacement in salt water == 35 cubic feet. 
1 fathom = 6 feet. 

1 cable length = 120 fathoms. 

THE METRIC STANDARDS OF WEIGHTS AND MEASURES. 

The metric unit of length is the metre = 39.37 inches. 

The metric unit of weight is the gram = 15.432 grains. 

The following prefixes are used for subdivisions and multiples . 
Milli = yoV(T» Centi = y^, Deci = y^' I^^ca = 10, Hecto — 100, 
Kilo = 1000, Myria = 10,000. 

Measures of Length. 

1 metre = 39.37 in., or 3.28083 ft., or 1.09361 yd. 

.3048 " =1 foot. 

1 centimetre = .3937 inch. 
2.54 centimetres = 1 inch. 

1 millimetre = .03937 inch, or -}^ inch nearly. 
25.4 millimetres = 1 inch. 
1 kilometre = 3280.83 ft. , or 1093.61 yds., or 0.62137 mill. 

Measures of Surface. 

1 square metre = 10.764 square feet or 1.196 sq. yd. 

.836 '♦ *' =1 sq. yd. 

.0929 *' *' =1 sq. ft. 

1 ** centimetre = .155 sq. in. 

6.452 *' centimetres = 1 sq. in. 
1 square millimetre = .00155 sq. in. 



WEIGHTS AND MEASURES. 393 

645.2 square millimetres = 1 sq. in. 

1 centiare = 1 sq. metre = 10.764 sq. ft. 

1 are =1 sq. decametre = 1076.4 *' ** 

1 hectare = 100 ares = 107641 '* ** 

= 2.4711 acres. 

1 square kilometre = .386109 sq. mile = 247.11 *' 
1 square myriametre = 38.6109 ** " 

Measures of Volume. 

1 cubic metre = 35.314 cu. ft. = 1.308 cu. yd. 

.7645 «* '* =1 cu. yd. 

.02832 ** ** = 1 cu. ft. 

1 ** decimetre = 61.023 cu. in. = .0353 cu. ft. 

,48.32 '* ** =1 cu. ft. 

1 " centimetre = .061 cu. in. 

16.387 " " = 1 cu. in. 

1 .i .. -- 1 millimetre = .061 cu. in. 

1 centilitre = .610 cu. in. 

1 decilitre = 6.102 " '' 

1 litre =1 cubic decimetre = 61.023 ** •* = 1.05671 quarts.* 

1 hectolitre or decistere = 3.314 cu. ft. = 2.8375 bushels. 

1 stere, kilolitre, or cubic metre = 1.308 cu. yd. = 28.37 bush. 

Measures of Capacity. 

1 litre = 1 cubic decimetre = 61.023 cu. in. 

= .03531 cu. ft. 

= .2642 gall. 

= 2.202 lbs. of water at 62* F. 
28.317 litres = 1 cu. ft. 
4.543 ** =1 gallon (British). 
3.785 ** =1 •' (American). 

Measures of Weight. 

1 gramme = 15.432 grains. 

.0648 " = 1 grain. 

28.35 *' = 1 ounce avoirdupois. 

1 kilogramme = 2.2046 lbs. 

.4536 *• = lib. 

1 tonne or metric ton 
1000 kilogrammes 

1016 ** = 1 ton of 2240 lbs, 



I = 2204.6 lbs. or .9842 ton of 2240 lbs. 



394 



WEIGHTS AN^D MEASURES. 



Table 79. 



i 



INCHES AND THEIR EQUIVALENT DECIMAL VALUES liN PARTS 
OP A FOOT. 



In. 





1 


2 


3 


4 


5 1 6 


7 


8 


9 


10 


11 





Foot 


.0833 


.1667 


.2500 


.a333 


.4167 .5000 


.5833 


.6067 


.7500 .8333 


,9167 


n'- 


.Q{)'2(i 


.0859 


.1693 


.2526 


.3:359 


.4193 .5026 


.5859 


.6693 


.7526 .8359 


.9193 


tV 


.0052 


.0885 


.1719 


.2552 


.3385 


.J219 .5052 


.5885 


.6719 


.7552 


.8885 


.9219 


^i 


.0078 


.0911 


.1745 


.2578 


.3411 


.4245 .5078 


.5911 


.6745 


.7578 


.8411 


.9245 


\ 


.0104 


.0938 


.1771 


.2604 


.3438 


.4271 .5104 


.5938 


.6771 


.7604 


.8438 


9271 




.0180 


.0964 


.1797 


.2630 


.3464 


.4297 5130 


.5964 


.6797 


.7630 


.8464 


.9297 


3 


.0156 


.0990 


.1823 


.2656 


.3490 


.4323 .5151; 


.5990 


.6823 


.7656 


.8490 


.9323 


/l. 


.0182 


.1016 


.1849 


.2682 


.3516 


.4349 .5182 


.6016 


6849 


.7682 


.8516 


.9349 


1 


.0208 


.1042 


.1875 


.2708 


.3542 


.4375'. 5208 


.6042 


.6875 


.7708 


.8542 


9375 


9 


.0284 


.1068 


.1901 


.2734 


.3568 


.4401 .5234 


.6068 


.6901 


.7734 


.8568 


.9401 


5 


0260 


.1094 


.1927 


.2760 


.3594 


.4427 .r 260 


.6094 


.6927 


.7760 


.8594 


.9427 


11 


.0286 


.1120 


.1953 


.2786 


.3620 


.4453 .5286 


.6120 


.6953 


.7786 


.8620 


.9453 


V 


.0313 


.1146 


.1979 


.2813 


.3646 


.4479!. 531 3 


.6146 


.6979 


.7813 


.8646 


,9479 




.0339 


.1172 


.2005 


.2839 


.3672 


.4505 .5339 


.6172 


.7005 


.7839 


.8672 


.9505 




.0365 


.1198 


.2031 


.2865 


.3698 


.45311.5365 


.6198 


.1031 


.7865 


.8698 


.9531 


M 


.0391 


.1224 


.2057 


.2891 


.3724 


.4557 .5391 


.6224 


.7057 


.7891 


.8724 


.9557 


i 


.0417 


.1250 


.2083 


.2917 


.3750 


.4583L5417 


.6250 


.7083 


.7917 


.8750 


,9583 


h^ 


,0443 


.1276 


.2109 


.2943 


.3776 


.4609 .5443 


.6276 


.7109 


.7943 


.8776 


.9609 




,0469 


1302 


.2135 


.2969 


.3802 


46351.5469 


. 6302 


.7135 


.7969 


.8802 


9635 


19 


.0495 


.1328 


.2161 


.2995 


.3828 


.46611.5495 


.6328 


.7161 


.7995 


8828 


.9661 


5 


.0521 


.1354 


.2188 


.3021 


.3854 


.4688 .5521 


.6354 


.7188 


.8021 


.8854 


9688 


21 


.0547 


.1380 


.2214 


.3047 


.3880 


.47141.5547 


.6380 


.7214 


.8047 


.8880 


.9714 


11 


.0573 


.1406 


.2240 


.3073 


.3906 


.4740, .5573 


.6406 


.7240 


.8073 


.8906 


.9740 


§5 


.0599 


.1432 


.2266 


.3099 


.3932 


.4766 '.5599 


.6432 


.7266 


.8099 


.8932 


.9766 


f 


,0625 


.1458 


.2292 


.3125 


.39.58 


.4792'. 5625 


.6458 


.7292 


.8125 


.8958 


.9792 


M 


.0651 


.1484 


.2318 


.3151 


.3984 


.4818 .5651 


.6484 


.7318 


.8151 


.8984 


.9818 


13 


.0677 


.1510 


.2344 


.3177 


.4010 


.4844 .5677 


.6510 


.7344 


.8177 


.9010 


9844 


27 


.0703 


.1536 


.2370 


.3203 


.4036 


.4870 .5703 


. 6536 


.7370 


.8203 


.9036 


,9870 


7 


0729 


.1563 


.2396 


.3229 


.4063 


.4896: .5729 


.6563 


.7396 


.8229 


.9063 


.9896 


2^ 


0755 


.1589 


.2422 


.3255 


.4089 


.4922 '.5755 


.6589 


.7422 


.8255 


.9089 


.9922 


IB 


.0781 


,1615 


.2448 


.3281 


.4115 


.4948 .5781 


.6615 


.7448 


.8281 


.9115 


.9948 


.0807 


.1641 


.2474 
2 


.3307 


.4141 


.4974 


.5807 


.6641 

7 


.7474 


.8307 
9 


.9141 
10 


.9974 
11 





1 


3 


4 


5 


6 


8 



DECIMAL EQUIVALENTS FOR FRACTIONS OF AN INCH. 



1/64 015625 

1/32 03125 

1/16 0625 

3/32 09875 

^ 1250 

5/32 1563 

3/16 1875 

7/32 187 



H 2500 

9/32 28125 

5/16 3125 

n/32 34375 

% 3750 

13/32 40625 

7/16 4375 

15/32 46875 



]4 5000 

17/32 53125 

9/16 5625 

19/32 59375 

% 6250 

21/32 65625 

11/16 6875 

.. .71875 



H 7500 

25/32 78125 

13/16 8125 

27/32 84375 

% 8750 

29/32 90625 

15/16 9375 

31/32 96875 



SPECIFIC GRAVITY. 395 



Specific Gravity. 

By specific gravity is meant the weight of a substance com- 
pared with the weight of water, takiug equal volumes of each. 
Water is adopted as the standard of gravity ; as a cubic foot of it 
at 62° F weighs 997.68 ounces avoirdupois, its weight is taken as 
the unit or approximately 1000. A cubic foot of cast iron 
weighs about 7i times as much as a cubic foot of water, but a 
cubic foot of cork weighs less than one-fourth as much as a 
cubic foot of water, and so the specific gravity of cast iron is set 
down as 7.5, and that of cork as 0.24. 

To ascertain the specific gravity of a solid body heavier than 
water, weigh it both in and out of water, and note the differ- 
ence ; then as weight lost in water is to whole weight so is 1000 
to specific gravity of the body, or 

W X 1000 
W-w - ^' 

TT^nd w representing weights out of and in water and G specific 
gravity. 

If the substance be lighter than water sink it by means of a 
heavier substance and deduct weight of the heavier substance. 

Weight of a cubic foot in pounds = specific gravity X 62.425, 
or specific gravity X 1000 and divided by 16 = weight in pounds. 



396 



SPECIFIC GRAYITY. 



Table 80. 

SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. 



Acacia-wood 

Acetone 

Acid, acetic, monohydrated 

" " greatest density 

" arsenic 

" arsenious 

" benzoic 

" boracic, crystallized 

fused 

" carbonic 

** chlorohydric, concentrated liquid. 

" citric 

" cyanohydric 

" formic 

*' fluoric 

*' hydrochloric (muriatic) 

*' hyponitric 

*' hyposulphuric, most concentrated . 

*' molybdic 

** nitric, fuming 

*' *' of commerce 

" *' tetrahydrated 

" oleic » 

" phosphoric, liquid 

*' " solid 

" silicic, quartz 

** ** agate 

** *' opal, hydrated silica 

" sulphuric, most concentrated 

** sulphurous 

" tannic 

*' tartaric 

*' telluric 

*' tellurous 

Agate 

Air at 60° F., barometer 30" 

Alabaster 

Alcohol, absolute, 60° 

*' greatest density 

*' of commerce 

'* proof spirit , 

Aldehyde , 

Alder- wood 

Alum. . . . < , 

i corundum I 

Alumina •< sapphire > , 

( ruby ) 

" emery ,... 

Aluminate of magnesia (spinel) 

" *' zinc 

Aluminium 

Amber 

Ambergris 

Amethyst, common , 

" oriental . 

Amanthus, .313 to 1.000 , 

Ammonia, aqueous 

Antimony, cast, 6.67 to 6.75 



Specific 
Gravity. 



.7.50 

.792 
1.068 
1.079 
3.391 
3.782 

.667 
1.479 
1.803 

.0019: 
1.208 
1.034 

.696 
1.116 
1.060 
1.200 
1.451 
1.347 
3.460 
1.451 
1.220 
1.420 

.898 
1.558 
2.800 
2.653 
2.615 
2.250 
1.841 
2.210 



2.615 

.001205 

2.700 

.792 

.927 

.834 

.916 

.790 

.800 
1.714 

4.160 

3.900 
3.700 
4.700 
2.600 
1.078 

.866 
2.750 
3.391 

.657 

.857 
6.710 



Weight 

of a Cubic 

Foot in 

Pounds. 



SPECIFIC GRAVITY. 



397 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Antimony, native 

Apple-wood . 

Aqua f ortis, double 

*' *' single 

Arragonite 

Arsenic 

Asbestos, starry 

Ash, perfectly dry, average 

" American, white, dry , 

Asphaltum, .905 to 1.65 

Azure, stone 

Bamboo , 

Barytes, sulphate of, 4 to 4.558 

" carbonate of, 4.1 to 4.6 ..... . 

Barium 

Basalt, 2.421 to 3.000 

Bathstone (oolite) 

Bay tree- wood 

Beech-wood, .852 to .690 

*' " perfectly dry , 

Beer 

Beeswax , ).. 

Beryl, oriental 

*' occidental , 

Bichloride of mercury 

Bismuth 

Bisulphide of mercury 

*' '* tin 

Birch 

Bitumen, liquid 

Blood, human 

*' crassamentum of 

Borate of magnesia (boracite) — . . . . . 

Brandy 

Brass (copper and zinc), cast, average 

'' copper 67, zinc 33 parts 

*' 84, time 

" rolled or plate 

" wire 

Brick, pressed 

common, 1.367 to 1.40 

fire 

" work in cement 

" " in mortar 1.6 to 2 

*' soft 

Bromine 

Bronze, copper 8 parts, tin 1 

Bullet-wood 

Butter 

Butternut- wood 

Cadmium 

Calcite, transparent, 2. .52 to 2.73 

Calcium 

Cainpeachy wood 

Camphor 

Caoutchouc (india-rubber). , . . 



Specific 
Gravity. 



6.670 

.793 

1.300 

1.200 

2.900 

5.673 

3.073 

.752 

.610 

1.277 

2.850 



.400 
.279 
.350 
.470 
710 
,100 
.822 
.771 
.624 
.034 
.965 
,594 
,723 
,420 
,822 
124 
415 
,567 
848 
,053 
245 
,500 
,924 
100 
820 
832 
380 
214 
400 
633 
201 
,800 
800 
600 
000 
500 
.9-18 
.942 
.376 



8.690 

2.620 

2.580 

.913 

.998 

.903 



Weight 

of a Cubic 

Foot in 

Pounds. 



417.9 
49.0 
81.25 
75.00 
181.25 
354.6 
192.1 
47.0 
38.15 
80.0 
178.15 



25.0 

267.3 

272.0 

29.4 

169.4 

131.25 
61.4 
48.2 
39.0 
64.62 
60.31 

223.4 

170.2 

338.75 

614.0 

507.75 

276.0 

354.4 
53.00 
65.875 
77.8 

156.25 
57.75 

506.0 

488.75 

552.0 

524.0 

513.4 

150.0 

102.1 

137.6 

112.5 

112.5 

100.0 

187.5 

531.25 
58.0 
58.875 
23,5 



543.7 
163.75 
92.5 
57.0 
62.4 
56.4 



398 



SPECIFIC GRAYITY. 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. {Continued.) 



Carbon, diamond 

"■ grapliite 

Carbonate of baryta 

'* " iron (iron spar) 

*' " lead (white lead) 

*' " lime (arragonite) 

" •* " (Iceland spar) 

** *' magnesia (giobertite) 

*' " manganese , 

** " strontia 

Carnelian, speckled 

Cedar, wild 

" Palestine ... 

" Indian 

Cement, Am. hydraulic Rosendale, loose 

" " " well shaken 

** ** *' thoroughly shaken 

" a struck bushel loose 75 lbs. 

" " " well shaken 88 lbs. 

** " " packed for sale 100 lbs. 

'* 1 barrel contains 3 struck bushels, or 3 

cu. ft. packed. 
" Portland, about 110 lbs. bushel, average. 

" Roman, '' " " " *' 

Chalcedony, common, 2.6 to 2.65 

Chalk, 2.252 to 2.657 

Charcoal of pine 

** fresh burned 

" of oak 

" of soft wood 

triturated 



Cherry . 

*' well seasoned 

Chestnut, perfectly dry 

Chromium . . 

Chloride of ammonium (sal ammonia). 

'' " barium 

" *' calcium 

" *' silver 

** ** sodium 

" ** potassium 

Chromate of lead 

'* *' potash 

Chrysolite, 2.782 to 3.400 



Cider. 

Cinnabar 

'' from Almaden. ... 

Citron-wood 

Clay, dry potter's, 1.8 to 2.1 . . 

'' *' in loose lumps 

'' with gravel 

Coal, anthracite, 1.436 to 1.64 

*' a solid yard makes 1% yds when broken for use 

*' cannel, 1.238 to 1.318 

•' caking 

*' bituminous, 1.2 to 1.5 

• ' broken, loose 

" a heaped bushel 70 to 78 lbs. 

*• a ton occupies from 43 to 48 cu. ft, 
Cobalt 



Specific 
Gravity. 



3.530 
3.500 
4.300 
3.850 
6.730 
2.946 
2.723 
2.880 
3.550 
3.650 
2.613 
.596 
.613 
1.315 



1.300 

1.560 

2.625 

2.454 

,441 

.380 

1.573 

.280 

1.380 

.715 

.672 

.660 

5.900 

1.520 

3.900 

3.200 

5.548 

2.100 

1.836 

6.600 

2.700 

3.091 

1.080 

8.098 

6.920 

.726 

1.900 



2.480 
1.538 



1.278 
1.277 
1.350 



8.600 



SPECIFIC GRAVITY. 



399 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Cobalt, cast , 

Cocoa- wood 

Coke 

" loose, of good coal 

*' National of Va 

" a heaped bushel 35 to 42 lbs. 

" a ton 80 to 97 cu. ft 

Colurabium 

Concrete, mean 

Copper, cast 

*' rolled , 

" wire 

Copal 

Coral, red 

" white 

Cork 

Cornelian 

Corundum 

Crab-tree 

Cypress-tree 

'* " well seasoned 



Deal- wood, Christiania 

Deutiodide of mercury 

Deutoxide of mercury 

" "copper , 

*' "tin 

Diamond, oriental, colorless 

" " colored, average 

*' Brazilian . 

'• " colored 

Dogwood 

Dolomite, 2.54 to 2.83 

Dragon's blood (a resin) 



Earth, dry common loam, loose. 

" " " soil 

" loose dry 

** " . slightly moist 

*' shaken, more " 

" fluid mud 

*' moist sand 

" mould, fresh 

" rammed 

*' rough sand . 

" with gravel 

Ebony, American 

*' Indian 

Egg 

Elker-wood 

Elm, perfectly dry 



Emerald 

Emery 

Ether, acetic 

*' chlorohydric 

*' muriatic 

** nitric 

" sulphuric 



Specific 
Gravity. 



7.812 
1.040 
1.000 



.746 



6.000 

2.000 

8.788 

8.950 

8.880 

1.045 

2.700 

2.550 

.240 

2.613 

3.710 

.765 

.644 

.441 



6.320 
11.000 
6.130 
6.700 
3.521 
3.536 
3.444 
3.550 
.756 
2.685 
1.204 



280 
194 
500 



,050 
,050 
,600 
920 
,020 
.331 
,209 
,090 
,695 
,570 
,671 
,680 
,000 
,868 
,874 
,729 
.908 
.715 



Weight 

of a Cubic 

Foot in 

Pounds. 



488.25 
65.0 
62.5 
23-32 
46.62 



375.0 

125.0 

549.25 

560.0 

555.0 

65.3 
168.75 
160 

15.0 
163.3 
232.0 

47.81 

40.25 

27.6 

43.0 
395.0 
687.5 
383.12 
418.75 
220.1 
221.0 
215.25 
222.0 

47.25 
168.0 

75.25 

72-80 

1371^ 
93.75 
70-76 
75-90 

104-112 

1281^ 

1281^ 

100.0 

120.0 

l26^ 

SQVe 

75^ 

68.0 

43.4 

35.6 

42.0 
167.5 
250.0 

54.1 

54.6 

45.6 

56.75 

44.7 



400 



SPECIFIC GRAVITY. 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Fat of beef 

" " hogs 

" " mutton 

Feldspar, 2.438 to 2.700 

Filbert-wood 

Fii-, Norway 

Fiiestone 

Flint, black 

" white — 

Fluoride of calcium (fluor spar). 

Fluorine 

Fusel oil 



Gamboge 

Garnet, precious, 4. to 4.23 

" common, 3.576 to 4 

Glass, 2.50 to 3.45 

" bottle 

*' common window, crown 

" thick flooring , 

*' green 

•* flint, 2.76 to 3.00 . 

*• optical 

" white 

Gneiss, conmion, 2.62 to 2.76 

" in loose piles 

" hornblendic 

Granite, Egyptian red 

'' Patapsco 

*' Old Dominion, Va 

*' Quincy 

" Scotch 

" Susquehanna, Pt. Deposit. 

Gravel, about equal to sand . . 

Greenstone (trap), 2.8 to 3.2 

" in loose piles 

Grindstone 

Gold, cast pure, 24 carat 

'' native pure 

" hammered pure, 19.4 to 19.6. . 

" 22 carat 

" 20 '* 

Gum Arabic 

Gum-tree, blue 

" " water 

Gunpowder, loose 

shaken . 



solid 5 S[. 



Gutta-percha 

Gypsum (plaster of Paris), average 

" in lumps 

" ground, loose (struck bushel 70 lbs.). 

" " well shaken 80 lbs 

*' *' thoroughly shaken 90 lbs. . . 



Hackmatack- wood . 
Hazel-wood 



Specific 
Gravity. 



.923 



2.509 

.690 

.512 

1.800 

2.582 

2.504 

3.200 

1.320 

.808 



.222 

kll5 
1.288 
1.975 
1.732 
1.520 
1.530 
1.642 
1.880 
!.450 
!.892 
1.690 



80 

654 

640 

630 

652 

625 

704 

749 

000 



143 
258 
320 
,500 
,486 
709 
,452 
843 
,000 
.900 
.000 

.675 

.980 
.305 



.592 



SPECIFIC GRAVITY. 



401 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Hawthorn-wood 

Heliotrope (bloodstone) -j I' I^qq y . 

Hemlock 

Hickory, pignut 

*' shell-bark 

*' red 

Holly 

Hone, white 

Honey 

Honeystone or mellite 

Horn 

Hornbeam-wood 

Hornblende 

black, 3.1 to 3.4 

Hornstone, 2.533 to 2.810 

Hyacinth, 4 toS4.78 

?Iydrogen gas 



Ice at 32^ F 

India-rubber 

Indigo 4 

/odide of potassium 

'' "silver ,., 

" " lead 

Iodine 

Iridium, cast by electric battery 

" hammered 

Iron cast 6 9 to 7.4 

'* ' at 450 lbs. to the foot, 8601.6 cu. in. wili make 
a ton. 

*' wrought, 7.6 to 7.9 

** magnetic oxide 

** cast, gun-metal 

** hot-blast 

** cold-blast 

" wire .... , 

** rolled plates 

*' large rolled bars 

Ironstone, 3.28 to 3.57 

Iron wood 

Isinglass 

Ivory 



Jackwood 

Jasmine 

Jasper, 2.358 to 2.816. 

Jet 

Juniper 



Lancewood 

Larch-wood, 5.44 to 5.( 

Lard 

Lead, cast 

*' rolled 

Lemon-tree 

Ligiium-vit8B . 



Specific 
Gravity. 



.910 

2.664 

.368 
.792 
.690 

.838 

.760 

2.876 

1.450 

1.620 

1.689 

.760 

3.540 

3 2.^0 

2.671 

4.390 

.000089 



.920 

.903 

1.009 

3.000 

5.614 

6.100 

4.948 

18.680 

23.000 

7.150 



7.770 
5.400 
7.308 
7.065 
7.218 
7.774 
7.704 
7.690 
3.475 
1.150 
1.111 
1.825 



.670 
.770 

2.587 

1.300 

.566 



.720 

.552 

.947 

11.352 

11.3S8 

1.333 



Weight 

of a Cubic 

Foot in 

Pounds. 



56.87 
166.5 

23.0 

49.5 

43.12 

52.375 

47.5 
179.75 

90.62 
101.25 
105.56 

47.0 
221.25 
203.0 
167. 
278.1 
.0056 



57.5 
56.437 
63.06 
187.5 
350.9 
381.25 
309.25 
1167.5 
1437.5 
446.0 



485. 

337.5 

456.7 

441.6 

451.1 

486.0 

481.15 

480.0 

217.2 

71.0 

69.437 
114.062 



42.0 
48.125 
161.7 
81.25 
35.37 



45.0 
34.5 
59.2 
709.5 
712.0 
43.94 
83.31 



402 SPECIFIC GRAVITY. 

SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Lime- wood 

Lime, ordinary quick 

'* hydraulic 

" ground, loose, struck bushel 71 lbs 

" " well shaken 80 lbs ., 

" " thoroughly shaken 93% lbs 

Limestones and marbles, 2.85 to 2.65 , 

Limestones and marbles, one cu. yd. solid makes 

about 1.9 yds. loose, or 1% yds. piled when .571 is 

solid and .429 voids. 

Linden-wood , 

Lithium 

Locust- VA ood , 

Logwood , 



Magnesia, carbonate of 

" native hydrate of 

Magnetic oxide of iron 

Mahogany, .72 to 1 .063 

" Honduras 

*' Spanish 

Malachite, compact 

Manganese 

Maple-wood 

" bird's-eye 

Marble, Adelaide 

African 

*' Biscayan, black 

" Carrara . 

*' common 

*' Egyptian 

*' French 

" Italian, white 

" Parian 

** Vermont, white 

Marl, mean 

Masonry, of granite or limestone 

" " well-scabbled rubble, 1/5 mortar 

'• " granite, dry rubble , 

" roughly scabbled rubble, 34 to ^ mortar, 

" " " dry.... 

Masonry, at 155 lbs. per cu. ft., a cu. yd. weighs 

1.868 tons, and 14.45 cu. ft. = 1 ton. 
Masonrj'^ of sandstone about % less than the above. 

" " brickwork, pressed, fine joints 

*' " " medium 

" '* " coarse, soft bricks 

Masonry, at 125 lbs. per cu. ft., a cu. yd. weighs 
1507 tons, and 17.92 cu. ft. = 1 ton. 

Mastic 

" wood 

Melanite or black garnet 

Mercaptan 

Mercury at 0° C. or 32** F 

" - 40° F 

" -f 60° F 

" 112° F 

Mica. 2.75 to 3. 1 

Millstone 



Specific 
Gravity. 



.804 

.843 

2.745 



2.75 



.604 
.590 

.728 
.913 



2.400 
2.330 
5.400 

.892 

.560 

.852 

3.790 

8.000 

.750 

.576 

2.715 

2.708 

2.695 

2.716 

2.689 

2.668 

2.649 

2.708 

2.838 

2.650 

1.750 



1.074 
.849 

3.750 
.804 
13.598 
15.632 
18. 580 
13.370 

2.930 

2.484 



SPECIFIC GRAVITY. 



403 



I 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. ^Continued,) 



Milk..... 

Mineral pitch or asphaltum, .905 to 1.650. 

'' tallow 

Molybdenum 

Molybdate of lead 

Mortar, hardened, 1.4 to 1.9 

Mud, dry close 

" wet, moderately pressed 

" fluid 

Mulberry- wood 

" Spanish 

Myrrh 



Naphtha 

Nickel 

'' cast 

Nitrate of baryta 

" " lead 

'* *' potash 

** *' strontia 

Nitre 

Nitrogen (about 1/35 lighter than air) . 



Oak, African 

" Canadian 

" Dantzic 

" English... 

" green 

*' heart (60 years old) . 

*' live, green 

" " seasoned 

*' white, dry 

" red, black, etc 

Obsidian . 

Oil of amber 

" " aniseseed 

*' " sweet almonds 

" " bitter almonds 

" " car ra way -seed 

*' *' cinnamon 

** *' citron 

'* " cloves 

" " codfish 

" " cotton-seed 

" " cumin 

'* " hemp-seed 

*' '• lavender 

" " linseed 

** " naphtha 

" *' olive 

'* *' palm 

" *' petroleum 

** " poppy-seed 

*' " rape seed 

" " sunflower 

** '* spirea 

" " turpentine 

*' " whiile 



Specific 
Gravity. 



1.030 
1.277 
.770 
8.600 
6.700 
1.650 



.561 

.897 
1.360 



.848 
8.666 
8.279 
3.185 
4.400 
1.930 
2.890 
1.900 



.823 
.872 
.759 
.932 
.146 
.170 
.260 
.068 
.860 



2.359 



.932 
.043 
904 
.010 

.847 
.036 
.923 



.969 
.926 
.894 
.940 
.848 
.915 
.969 
.878 
.939 
.914 
.926 
.173 
.870 
.923 



Weight 

of a Cubic 

Foot in 

Pounds. 



64.4 

80.0 

48.1 
537.5 
418.75 
103.0 

80-110 
110-130 
104-120 

35.06 

56.06 

85.0 



52.9 
541.6 
517.3 
199.1 
277.5 
120.6 
180,6 
118.75 



51.437 
54.5 
47.43 
58.25 
71.625 
78.125 
78.75 
66.75 
53.75 
40.75 
128.7 
54.25 
61.625 
58.25 
65.2 
56.5 
63.1 
53.0 
64.7 
57.6 



60.6 

57.9 

56.0 

58.75 

53.0 

57.18 

60.56 

54.875 

58.7 

57 12 

57.875 

73 3 

54.37 

57.68 



404 



SPECIFIC GRAVITY. 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Oil of wormwood 

defiant gas 

Olive-wood 

Oolites or roestones, 1 .9 to 3.5 

Opal, precious 

common 

Opium 

Orange- wood 

Orpiment, 3.048 to 3.5 

Osmium 

Oyster-shell 

Oxide of bismuth 

" " silver 

'* *' zinc 

Oxygen gas (1/10 heavier than air). 



) ton. 



Palladium 

rolled 

Paving-stones 

Pearl-wood 

Pearl, oriental, 2.51 to 2.75 

Peailstone 

Peat, dry unpressed 

Peroxide of iron 

" " lead 

" " manganese 

" " titanium (rutile) 

Persimmon-wood 

Peruvian bark 

Petroleum 

Phosphorus 

Pine, Dantzic 

" Memel..., 

'• Riga 

" white, perfectly dry 

*' 1000 ft. b. m. weighs .9 

" yellow Northern, .48 to .62 

" 1000 ft. b. m. weighs 1.276 ton. 

" yellow Southern, .64 to .80 

" heart, unseasoned.. 

pitch 

Pitch 

Pitchstone, 1.92 to 2.72 

Piaster of Paris. 

Platinum , 

wire 

rolled 

' ' in grains, native 

" forged 

Plurn-wood 

Plumbago or graphite 

Pomegranate 

I'oon-wood 

P« >plar 

white 

Pi)rcelain, China 

" Sevres 

Porphyry, red 

' ' Seltzer 



Specific 
Gravity. 



.907 

.00127 

.923 
2.200 
2.114 
2.040 
1.336 

.705 
8.274 
10.000 
2.092 
8.968 
7.250 
5.600 

.00143 



11.300 
11.800 
2.416 
.661 
2.630 
2.340 



5.225 

9.200 

4.480 

4.250 

.710 

.784 

.878 

1.770 

.649 

.550 

.466 

.400 



.550 



.720 

1.040 

1.150 

1.150 

2.345 

1.176 

21.530 

21 .042 

22.060 

17.500 

20.336 

.785 

2.200 

1.351 

.580 

.383 

.529 

2.300 

2.145 

2.765 

1.003 



Weight 

of a Cubic 

Foot in 

Pounds. 



SPECIFIC GRAVITY. 



405 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Specific 
Gravity. 



Weight 

of a Cubic 

Foot in 

Pounds. 



Potassium at 59° F 

Powder, slightly shaken 

Proof spirit , . 

Protoxide of antimony 

" " copper 

" " lead, cast 

Protochloride of mercury 

Protoiodide of mercury 

Protosulphide of tin 

" " manganese. 
" " copper. .. . 
Pumice-stone, .792 to .914 



Quartz, common pure 

" finely pulverized, loose 

'* " " well shaken 

" ** " packed 

'* quarried loose, 1 part solid makes IJ^ loose, 
Quince- wood 



Realgar, 3.225 to 3.38 

Red lead 

Red oxide of manganese 

Resin or rosin , 

Rhodium 

Rock crystal 

Rosewood 

Rotten stone 

Ruby 

Ruthenium 



Salt 

Saltpetre 

Sand, pure quartz, dry and loose 

" struck bushel 112 to 133 lbs. 

" average 98 lbs. per cubic foot. 
Sand, a struck bush. = 122!.^ lbs., and 18.29 bush.= 1 

ton. A cu. yd. = 1.181 tons, and 22.86 ft. = 1 ton 
Sand, well shaken, struck bushel 123-147 lbs 

" " packed .., 

*' perfectly wet, drained off 

Sandstones, for building, dry, 2.10-2.73 

" piled, 1 measure solid = 1% 

Sapphire , 

'' oriental 

Sardonyx 

Sassafras- wood 

Satinwood 

Scammony of Smyrna ., 

Schorl : 

Sea-water ; 

Selenium 

Selenite of lead 

Serpentine, 2.264 to 3.00 

Sesquioxide of mangan se 

Shale, red or black 

Shingle (pebbles and band) 



1.000 
.916 
5.778 
5.300 
9.500 
7.140 
7.750 
5.267 
3.950 
5.690 



2.650 



.705 



3.278 
8.940 
4.722 
1.089 
10.650 
2.735 
.728 
1.981 
4.040 
8.600 



2.070 
2.090 
1.650 



2.410 



3.994 
4.100 
2.615 
.482 
.885 
1.274 
3.170 
1.026 
4.400 
7.690 
2.634 
4.810 
2.600 
1.420 



54.1 

62.5 

56.0 

361.0 

331.2 

593.7 

446.0 

484.4 

329.2 

247.0 

355.6 

55.8 



165.0 
90.0 
105.0 
112.0 



44.06 



204.7 
558.7 
295.1 

68.1 
665.6 
171.0 

45.5 
123.8 
252.5 
537.5 



129.4 
130.62 
90-106 



99-117 
101-119 
120-140 
150.0 

86.0 
237.1 
256.2 
163.4 

80.122 

55.315 

79.6 
198.1 

64.1 
275.0 
480.6 
164.6 
306.2 
162.5 

88.7 



406 



SPECIFIC GRAVITY. 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Specific 
Gravity. 



Silicate of zirconia 

Silver, pure cast 

' ' hammered 

" glance, 5.2 to 7.8 

Slate, 2.672 to 2.90 

'' purple 

" drawing . . 

Smalt 

Snow, freshly fallen 

" compacted by rain 

Soapstone or steatite, 2.65 to 2.80. , . 

Soap 

Sodium at 59° F 

Spar, fluor, 3.094 to 3.791 

'^ feld 

" calc, 2.62 to 2.837 

Spelter or zinc, 6.8 to 7.2 

Spermaceti 

Spruce 

Stalactite, 2.323 to 2.546 

Starch 

Steam 

Steel, 7.8 to 7.9 

" plates .. 

" soft 

" tempered and hardened 

*' wire 

Stone, Bath, Eng 

Blue Hill 

" Bluestone (basalt) 

*' Breakneck, N. Y 

*' Bristol, Eng 

" Caen, Normandy 

" common 

" Craigleth, Eng 

*' grind 

" Kentish rag 

Kips Bay, N. Y 

" Norfolk, Parliament House. 

" Portland, Eng 

*' rotten 

** sandstone (mean) 

'• Sydney 

Staten Island, N. Y 

•* SulHvan Co 

Strontium 

Sugar 

Sulphate of baryta (heavy spar) 

*' " strontia (celestine) 

" " lead 

" *' silver 

" " lime (anhydrite) 

" '* (gypsum) 

" " potash . 

** " soda, anhydrous 

Sulphide of antimony 

" •' bismuth 

" " carbon 

" l.a.l (g.ilena) 

" " nwilybflennm 

'• " silver 



474 

511 
250 
791 
,784 
,110 
,440 



.730 

.071 

.972 

.442 

.700 

.729 

.000 

.943 

.500 

1.434 

.950 

.0088 

'.850 

'.806 

.833 

.818 

'.847 

.961 

t.640 

1.625 

1.704 

1.510 

1.076 

!.520 

:.316 

M42 

1.651 

1.759 

304 

,368 

981 

,400 

237 

976 

688 

540 

606 

700 

950 

300 

340 

900 

305 

400 

630 

334 

540 

•2G3 

580 

601) 

-M) 



SPECIFIC (GRAVITY. 



407 



SPECIFIC GRAVITY AND WEIGHT OF MATERIALS. (Continued.) 



Sulphide of zinc (blende) 
Sulphur, native 
'' fused 
Sycamore-wood 

J mean 

*' black 

Tallowo 

Tamarack-tree 

Tar 

Teak (African oak) 6.57 to 7.45 

Tellurium 

Thalium 

Tile 

Tin, Cornish hammered 

" " pure 

Topaz, oriental 
Tourmaline 
Trap 
Tungsten 
Turf or peat, dry and unpressed 
Turquoise, 2.50 to 3.00 




150.0 
L>H4 

449 4 



408 



MENStTRATIOK. 

Mensuration. 

Mensuration of Surfaces. 



1 



Area of any parallelogram 
Area of any triangle 
Area of any circle 
Area of sector of circle 
Area of segment of circle 

Area of parabola 
Area of ellipse 

Area of cycloid 

Area of any regular polygon 



Surface of cylinder 

Surface of cone 

Surface of sphere 
Surface of frustum 

Surface of cylindrical ring 

Surface of segment 



: base X perpendicular height, 
base X i perpendicular height, 
diameter^ x .7854. 

: arc X i radius. 

area of sector of equal radius 
less area of triangle. 

: base X f beight. 

: longest diameter X shortest di- 
ameter X .7854. 
area of generating circle X 3. 

: sum of its sides X perpendicular 
from its centre to one of its 
sides ^- 2. 
area of both ends + length X 
circumference. 

: area of base + circumference of 
base X i slant height. 

: diameter^ X 3.1415. 

: sum of girth at both ends X i 
slant height + area of both 
ends. 

: thickness of ring added to the 
inner diameter X by the thick- 
ness X 9.8698. 

: height of segment X whole cir- 
cumference of sphere of which 
it is a part. 



POLYGONB. 

1. To find the area of any regular polygon. Square one of its 
sides, and multiply said square by the number in column 1 of the 
following table. 

2. Having a side of a regular polygon, to find the radius of a 
circumscribing circle. Multiply the side by the corresponding 
number in column 2. 



MENSURATION. 



409 



3. Having the radius of a circumscribing circle, to find the 
side of the inscribed regular polygon. Multiply the radius by 
the corresponding number in column 3. 



Num- 
berof 




1 


2 


3 


Angle con- 


Name of Polygon. 








tained be- 
tween Two 


Sides. 




Area=<S2X. 


= 6'X. 


Side = BX. 


Sides. 


3 


j Equilateral } 
I triangle ) 


.433 


.5774 


1.732 


60° 


4 


Square 


1.0 


.7071 


1.4142 


90° 


5 


Pentagon 


1.7205 


.8507 


1.1756 


108° 


6 


Hexagon 


2.5891 


1.0 


1.0 


120° 


7 


Heptagon 


3.6339 


1.1524 


.8678 


128.57° 


8 


Octagon 


4.8284 


1.3066 


.7654 


135° 


9 


Nonagon 


6.1818 


1.4619 


.684 


140° 


10 


Decagon 


7.6942 


1.618 


.618 


144° 


11 


Undecagon 


9.3656 


1.7747 


.5635 


147.27* 


12 


Dodecagon 


11.1962 


1.9319 


.5176 


150° 



In the heads of the columns in above table 8 = side, and 
R = radius. 



Cylinder 

Sphere 

Segtnent of sphere 



Cone or pyramid 
Frustum of a cone 



Mensuration of Solids. 

= area of one end X length. 
= cube of diameter X .5236. 

square root of the height added to three 

times the square of the radius of 

base X by height and X .5236. 
area of base X i height, 
product of diameter of both ends + 

sum of their squares X perpendicular 

height X .2618. 
Frustum of a pyramid = sum of the areas of the two ends -|- 

square root of their product X i of 

the perpendicular height, 
area of base X J height. 
I height X sum of the areas of the two 

ends, 
thickness + inner diameter X square 

of the thickness X 2.4674. 



Solidity of a wedge 
Frustum of a wedge 

Solidity of a ring 



410 



MENSURATION. 
Polyhedrons. 



1 



No. of 
Sides. 



Names. 



12 
20 



Tetrahedron . . . 
Hexabedrou. . . 
Octahedron . . . 
Dodecahedron. 
Icosahedrou.... 



1 


2 


3 


Radius of 


Radius of 


Area of 


Circum- 


Inscribed 


Surface. 


scribed 


Circle. 




Circle. 






.6124 


.2041 


1.7320 


.866 


.5 


6. 


.7071 


.4082 


3.4641 


1.4012 


1.1135 


20.6458 


.951 


.7558 


86.602 



4 

Cubic 
Coutents. 



.1178 
1. 

.4714 
7.6631 
2.1817 



Side is length of linear edge of any side of the figure. 

Radius of circumscribed circle = side X the number in col- 
umn 1 corresponding to the figure. 

Radius of inscribed circle = side X the number in column 2 
corresponding to the figure. 

Area of surface = square of side X the number in column 3 
corresponding to the figure. 

Cubic contents = cube of side X the number in column 4 cor- 
responding to the figure. 

Properties of the Circle. 

Diameter X 3.14159 = circumference. 

** X .8862 = side of an equal square. 

X .7071 = ** " '* inscribed square. 
Diameter^ X .7854 = area of circle. 

Radius X 6.28318 = circumference. 

Circumferences- 3.14159 = diameter. 

The circle contains a greater area than any plane figure 
bounded by an equal perimeter or outline. 

The areas of circles are to each other as the squares of their 
diameters. 

Any circle whose diameter is double that of another contains 
four times the area of the other. 

The area of a circle is equal to the area of a triangle whose 
base equals the circumference, and perpendicular equals the 
radius. 



MEKSURATION". 



411 



Table 81. 
AREAS AND CIRCUMFERENCE OP CIRCLES. 



Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


1/64 


.049087 


.00019 


2 % 


8.24668 


5.4119 


6 Vs 


20.8131 


34.472 


1/32 


.098175 


.00077 


11/16 


8.44303 


5.6727 




21.2058 


35.785 


3/64 


.147262 


.00173 


H 


8.63938 


5.9396 


% 


21.5984 


37.122 


1/16 


.196350 


.00307 


13/16 


8.83573 


6.2126 


7 


21.9911 


38.485 


3/32 


.2945-.'4 


.00690 


Vs 


9.03208 


6.4918 


Vi 


22.3838 


39.871 


% 


.892699 


.01227 


15/16 


9 22843 


6.7771 


/4 


22.7765 


41.282 


5/32 


.490874 


.01917 


3 


9.42478 


7.0686 


% 


23.1692 


42.718 


3/16 


.589049 


.02761 


1/16 


9.62113 


7.3662 


V2 


23.5619 


44.179 


7/32 


.687223 


.03758 


Vs 


9.81748 


7.6699 


V>> 


23.9546 


45.664 


9/32 


.785398 


.04909 


3/16 


10.0138 


7.9798 


% 


24.3473 


47.173 


.883573 


.06J13 


H 


10.2102 


8.29.58 


Vs 


24.7400 


48.707 


5/16 


.981748 


.07670 


5/16 


10.4065 


8.6179 


8 ^ 


25.1327 


50.265 


11/32 


1.07992 


.09281 


% 


10.0029 


8.946:2 




25.5254 


51.849 


% 


1.17810 


.11045 


7/16 


10.7992 


9.2806 


i 


25.9181 


53 456 


13/32 


1.27627 


.12<J62 


V2 


10.9956 


9.6211 


26.3108 


55.088 


7/16 


1.37445 


.15033 


9/16 


11.1919 


9.9678 


L^ 


26.7035 


56.745 


15/32 


1.47262 


.17257 


V8 


11.3883 


10.321 


% 


27.0962 


58.426 


L^ 


1.57080 


.19635 


11/16 


11.5846 


10.680 


% 


27.4889 


60.132 


17/32 


1.66897 


.22166 


V4 


11.7810 


11.045 


Vs 


27.8816 


61.862 


9/16 


1.76715 


.24850 


13/16 


11.9773 


11.416 


9 


28.2743 


63.617 


19/33 


1.86532 


.27688 


% 


12.1737 


11.793 


Vs 


28.6670 


65.397 


1.96350 


.30680 


15/16 


12.3700 


12.177 


Va 


29.0597 


67.201 


21/32 


2.06167 


.33824 


4 


12.5664 


12.566 




29.4524 


69.029 


11/16 


2.15984 


.37122 


1/16 


12.7627 


12.962 


i 


29.8451 


70.882 


23/32 


2.25802 


.40574 


Vs 


12.9591 


13.364 


30.2378 


72.760 


H 


2.35619 


.44179 


3/16 


13.1554 


13.772 


M 


30.6305 


74.662 


25/32 


2.45437 


.47937 


H 


13.3518 


14.186 


Vs 


31.0232 


76.589 


13/16 


2.55254 


.51849 


5/16 


13.5481 


14.607 


10 


31.4159 


78.540 


27/32 


2.05072 


.55914 


Vs 


13.7445 


15.033 


IX 


31.8086 


80.516 


% 


2.74889 


.60132 


7/16 


13.9408 


15.466 


\A 


32.2013 


82.516 


29/32 


2.84707 


.64504 


V2 


14.1372 


15.904 


% 


32.5940 


84.541 


15/16 


2.94524 


.69029 


9/16 


14.3335 


16.349 


Vs 


32.9867 


86.590 


31/32 


3.04342 


.73708 


Vs 


14.5299 


16.800 


33.3794 


88.664 


1 


3.14159 


.78540 


11/16 


14.72G2 


17.257 


H 


33.7721 


90.763 


1/16 


3.33794 


,88664 


V4 


14.9226 


17.721 


Vs 


34.1648 


92.886 


k 


3.53429 


.99402 


13/16 


15.1189 


18.190 


11 


34.5575 


95.033 


3/16 


3.73064 


1.1075 


Vs 


15.31.53 


18.665 


14 


34.9502 


97.205 


k 


3.92699 


1.2272 


15/16 


15.5116 


19.147 


tA 


35.3429 


99.402 


5/16 


4.12334 


1.3530 


5 


15.7080 


19.635 


% 


35.7356 


101.62 


V8 


4.31969 


1.4849 


1/16 


15.9043 


20.129 


L^ 


36.1283 


103.87 


7/16 


4.51604 


1.6230 


Vs 


16.1007 


20.629 


5/. 


36.5210 


106.14 


H 


4.71239 


1.7671 


3/16 


16.2970 


21.135 


H 


36.9137 


108.43 


9/16 


4.90874 


1.9175 


^ 


16.4934 


21.648 


Vs 


37.3064 


110.75 


V8 


5.10509 


2.0739 


5/16 


16.6897 


22.166 


12 


37.6991 


113.10 


11/16 


5.30144 


2.23f;5 


Vs 


16.8861 


22.691 


Vs 


38 0918 


115.47 


k 


5.49779 


2.4053 


7/16 


17.0824 


23.221 




38.4845 


117.86 


13/16 


5.69414 


2.5802 


V2 


17.2788 


23.758 


% 


38.8772 


120.28 


% 


5.89049 


2.7612 


9/16 


17.4751 


24.301 


V> 


39.2699 


122.72 


15/16 


6.08684 


2.9483 


Vs 


17.6715 


24.850 


% 


39.6626 


125.19 


2 


6.28319 


3.1416 


11/16 


17.8678 ■ 


25.406 


H 


40.0553 


127.68 


1/16 


6.47953 


3.3410 


H 


18.0642 


25.967 


Vs 


40.4480 


130.19 


^ 


6.67588 


3.5466 


13/16 


18.2605 


26.535 


13 


40.8407 


132.73 


3/16 


6.87223 


3.7583 


Vs 


18.4569 


27.109 


% 


41.2334 


135.30 


H 


7.06858 


3.9761 


15/16 


18.6532 


27.688 


H 


41.6201 


137.89 


5/16 


7.26493 


4.2000 


6 


18.8496 


28.274 


% 


42.0188 


140.50 


^% 


7.461 :>8 


4.4301 


% 


19.2423 


29.465 


^ 


42.4115 


143.14 


7.65763 


4.6664 


H 


19.6350 


30.680 


^ 


42.8042 


145.80 


^ 


7.85398 


4.9087 


4 


20.0277 


31.919 


i 


43.1969 


148.49 


9/16 


8.05033 


5.1572 


M 


20.4204 


33.183 


43.5896 


151.20 



412 



MENSURATION". 



AREAS AND CIRCUMFERENCE OF CIRCLES. (Continued.) 



Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


14 


43.98-23 


153.94 




44.3750 


156.70 


% 


44.7677 


159.48 


45.1604 


162.30 


1^ 


45.5531 


165.13 


% 


45.9458 


167.99 


% 


46.3385 


170.87 


% 


46 7312 


173.78 


15 


47.1239 


176.71 




47.5166 


179.67 


M 


47.9093 


182.65 


a^ 


48.3020 


185.66 


H 


48.6947 


188 69 


% 


49.0874 


191.75 


3^ 


49.4801 


194.83 


% 


49.8728 


197.93 


16^^ 


50.2655 


201.06 


^ 


50.6582 


204.22 


i 


51.0509 


207.39 


51.4436 


210.60 


iz 


51.8363 


213.82 


% 


52.2290 


217.08 


M 


52.6217 


220.35 


% 


53.0144 


223.65 


17 


53.4071 


226.98 


^ 


53.7998 


230.33 




54.1925 


233.71 


54.5852 


237.10 


/^ 


54.9779 


240.53 


% 


55.3706 


243 98 


yA 


55.7633 


247.45 


% 


56.1560 


250.95 


18 


56.5487 


254.47 




56.9414 


258.02 


1^ 


57.3341 


261.59 


^ 


57.7268 


265.18 


L^ 


58.1195 


268.80 


n^ 


58.5122 


272.45 


1 


58.9049 


276.12 


59.2976 


279.81 


19 


59.6903 


283.53 




60.0830 


287.27 


14 


60.4757 


291.04 


% 


60.8684 


294.83 


L^ 


61.2611 


298.65 


^ 


61.6538 


302.49 


1 


62.0465 


306.35 


62.4392 


310.24 


20 


62.8319 


314.16 


^ 


63.2246 


318.10 




63.6173 


322.06 


64.0100 


326.05 


LZ 


64.4026 


330.06 


1^ 


64.7953 


334.10 


H 


66.1880 


338.16 


65.5807 


342.25 


21 


65.9734 


346.36 


^ 


66.3661 


350.50 


i 


66.7588 


:^54.66 


67.1515 


358.84 


^ 


67.5442 


363.05 



Diam. 
In. 



% 



22 






23 



% 
V2 



24 



H 



25 



% 

% 
% 

6 



27 



M 

i 

^ 



% 



28 






% 



29 



% 



Cir- 

cumf. 

In. 



67.9369 

68.3296 

68.7223 

69.1150 

69.5077 

69 9004 

70.2931 

70.6858 

71.0785 

71.4712 

71.8639 

72.2566 

72.6493 

73.0420 

73.4347 

73.8274 

74.2201 

74.6128 

75.0055 

75.3982 

75.7909 

76.1836 

76.5763 

r6.9690 

77.3617 

77.7544 

78.1471 

78.5398 

78.9325 

79.3252 

79.7179 

80.1106 

80.5033 

80.8960 

81,2887 

81.6814 i 

82.0741 

82.4668 

82.8595 

83.2522 1 

83.6449 ' 

84.0376 I 

84.4303 i 

84.8230 I 

85.2157 I 

85.6084 

86.0011 I 

86.393S I 

86.7865 

87.1792 

S7.5719 ; 

87.9646 i 

88.3573 ! 

88.7500 ; 

89.1427 I 

89.5354 

89.9281 i 

90.3-J08 

90.7135 ! 

91.1062 ! 

91.4989 I 



Area. 


Diam. 


Sq. In.: 


In. 


367.28 


2914 


371.54 , 


% 


37 5. 8-^ ' 


/^ 


380.13 i 


5Z 


384.46 j 


% 


388.82 ; 


% 


393.20 ; 


30 


397.61 


M 


402.04 


H 


406.49 


3^ 


410.97 


/^ 


415.48 


% 


4-:o.oo 


M 


424.56 


% 


429.13 


31 


433.74 




438.36 


M. 


443.01 


% 


447.69 




452.39 


% 


457.11 


M 


461.86 


% 


466.64 


32 


471.44 


% 


476.26 




481.11 


% 


485.98 


}i 


490.87 


% 


495.79 




500.74 


% 


505.71 


33 


510.71 


% 


515.72 




520.77 


% 


525.84 


v^ 


530.93 


H 


530.05 


H 


541.19 


% 


546.35 


34 


551.55 


iz 


556.76 


/4 


562.00 


% 


567.27 


iz 


572.56 


% 


577.87 


% 


583.21 


ZA 


588.57 


35 


593.96 


% 


599.37 


H 


604.81 


% 


610.27 
615.65 


k 


621.26 


^ 


626.80 


% 


632.36 


36 


637.94 


% 


643.55 


/4 


649.18 


a^ 


654.84 


H 


660.52 


&^ 


666.23 


H 



Cir- 

ciimf. 

In. 



91.8916 
92 2843 
92.6770 
93.0697 
93.4624 
93.8551 
94.2478 
94.6405 
95.0332 
95.4259 
95.8186 
96.2113 
96.6040 
96.9967 
97.3894 
97.7821 
98.1748 
98 5675 
98.9602 
99.3529 
99.7456 
100.138 
100.531 
100.924 
101.316 
101.709 
102.102 
102.494 
102.887 
103.280 
103.673 
104.065 
104.458 
104.851 
105.243 
105.636 
106.029 
106.421 
106.814 
107.207 
107.600 
107.992 
108.385 
108.778 
109.170 
109.563 
109.956 
110.348 
110.741 
111.134 
111.527 
111.919 
112.312 
112.705 
113.097 
113.490 
113.88:3 
114.275 
114.668 
115.061 
115.454 



MENSUKATIOIS:. 



413 



AREAS AND CIRCUMFERENCE OF CIRCLES. (Continued.) 



Diam. 
In. 


Cir- 

cumf. 

In. 


36% 


115.846 


37 


Ii6.ti39 


Va 


116.632 




117.024 


a^ 


117.417 


/^ 


117.810 


5^ 


118.202 


% 


118.596 


% 


118.988 


38 


119.381 




119.773 


% 


120.166 


120.559 


^4 


120.951 


121.344 


121.737 


Vs 


122.129 


39 


122 522 


% 


122.915 


H 


123.308 




123.700 


i 


124.093 


124.486 


H 


124.878 


% 


125.271 


40 


125.664 


% 


126.056 


H 


126.449 




126.842 


v^ 


127.235 


% 


127.627 


3^ 


128.020 


% 


128.413 


41 


128.805 


14 


129.198 


il 


129.591 


8^ 


129.993 


L^ 


130.376 


% 


130.769 


H 


131.161 


Vs 


131.554 


42 


131.947 


Vs 


132.340 




132.732 


% 


133.125 


?3 


133.518 


% 


133.910 


V4 


134.303 


Vs 


131.696 


43 


135.088 


% 


135.481 


H 


135.874 


% 


136.267 




136.659 


137.052 


% 


137.445 


% 


137.837 


44 


138.230 


1^ 


13H.623 


/4 


139.015 


% 


139.408 



Area. 
Sq. In. 



1068.0 
1075.2 
1082.5 
1089.8 
1097.1 
1104.5 
11118 
1119.2 
1126.7 
1134.1 
1141.6 
1149.1 
1156.6 
1164.2 
1171.7 
1179.3 
1186.9 
1194.6 
1102.3 
1110.0 
1117.7 
1225.4 
1233.2 
1241.0 
1248.8 
1256.6 
1264.5 
1272.4 
1280.3 
1288.2 
1296.2 
1304.2 
1312.2 
1320.3 
1328.3 
1336.4 
1344.5 
1352.7 
1360.8 
1369.0 
1:^77.2 
1385.4 
1393.7 
H02.0 
1410.3 
1418 6 
1427.0 
1435.4 
1443.8 
1452 2 
1460.7 
1469.1 
1477 6 
1486.2 
1494.7 
1503.3 
1511.9 
1520.5 
1529.2 
1537.9 
1546 6 



Diam. 


Cir- 

cumf. 

In. 


Area. 


In. 


Sq. In. 


44^ 


139.801 


1555.3 


Vs 


140.194 


1564.0 


% 


140 586 


1572.8 


% 


140.979 


1581.6 


45 


141.372 


1590.4 


Vs 


141,764 


1599.3 


M 


142.157 


1608.2 




142.550 


1617.0 


IZ 


142.942 


1626.0 


% 


143.335 


1634.9 


'M 


143.728 


1643.9 


% 


144.121 


1652.9 


46 


144.513 


1661.9 


% 


144.906 


1670.9 


Va 


145.299 


1680.0 


% 


145.691 


1689.1 




146.084 


1698.2 


5/. 


146.477 


1707.4 


¥4 


146.869 


1716.5 


Vs 


147.262 


1725.7 


47 


147.655 


1734.9 


Vs 


148.048 


1744.2 


M 


148.440 


1753.5 


% 


148.833 


1762.7 




149.226 


1772.1 


% 


149.618 


1781.4 


H 


150.011 


1790.8 


% 


150.404 


1800.1 


48 


150.796 


1809.6 


Vs 


151.189 


1819.0 


M 


151,582 


1828.5 


¥s 


151.975 


1837.9 




152.367 


1847.5 


% 


152.760 


1857.0 


H 


153.153 


1866.5 


Vs 


153.545 


1876.1 


49 


153.938 


1885.7 


Vs 


154.331 


1895.4 


H 


154.723 


1905.0 




155.116 


1914.7 


/^ 


155.509 


1924.4 


% 


155.902 


1934.2 


% 


156.294 


1943.9 


Vs 


156.687 


1953.7 


50 


157.080 


1963.5 


Vs 


157.472 


1973.3 


H 


157.865 


1983.2 


% 


158.2.58 


1993.1 


V2 


158.650 


2003.0 


% 


159.043 


2012.9 


V4 


159.436 


2022.8 


Vs 


159.829 


2032.8 


51 


160.221 


2042.8 


Vs 


160.614 


2052.8 


V4 


161.007 


2062.9 


% 


161.399 


2073.0 


Vq 


161.792 


2088.1 




162.185 


2093 2 


% 


162.577 


2103.3 


Vs 


1()2.970 


2113.5 


52 


163.363 


2123.7 



Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


52% 


163.750 


2133.9 


lA 


164.148 


2144.2 


a^ 


164.541 


2154.5 


1^ 


164.934 


2164.8 


% 


165.326 


2175.1 


M 


165.719 


2185.4 


Vs 


166.112 


2195.8 


53 


166.504 


2206.2 


Vs 


166.897 


2216.6 


Va 


167.290 


2227.0 


Vs 


167.683 


2237.5 




168.075 


2248.0 


168.468 


2258.5 


4 


168.861 


2269.1 


Vs 


169.253 


2279.6 


54 


169.646 


290.2 


Vs 


170.039 


2300.8 


V4 


170.431 


2311.5 




170.824 


2322.1 


IZ 


171.217 


2332.8 


% 


171.609 


2343.5 


3/ 


172.002 


2354.3 


Vs 


172.395 


2365.0 


55 


172.788 


2375.8 


Vs 


173.180 


2386.6 


V4 


173.573 


2397.5 


Vs 


173.966 


2408.3 




174.358 


2419.2 


% 


174.751 


2430.1 


¥4 


175.144 


2441.1 


Vs 


175.536 


2452.0 


56 


175.929 


2463 




176.322 


2474.0 


lA 


176.715 


2485.0 


% 


177.107 


2496.1 


]Z 


177.500 


2507.2 


5^ 


177.893 


2518.3 


% 


178.285 


2529.4 


% 


178.678 


2540.6 


57 


179.071 


2551.8 


H 


179 463 


2563.0 




179.856 


2574.2 


3^ 


180.249 


2585.4 


LZ 


180.642 


2596.7 


% 


181.034 


2608.0 


¥4 


181.427 


2619.4 


Vs 


181.820 


2630.7 


58 


182.212 


2642.1 


LZ 


182.605 


2653.5 


M- 


182.998 


2664.9 


% 


183.390 


2676.4 


k 


183.783 


2687.8 


184.176 


2699.3 


i 


184.569 


2710.9 


184.961 


2722.4 


59 


185.354 


2734.0 


^ 


185.747 


2745.6 




186.139 


2757.2 


% 


186.532 


2768.8 


\j. 


186.925 


2780.5 


% 


187.317 


2792.2 



414 



MENSURATION. 



AREAS AND CIRCUMFERENCE OF CIRCLES. (Continued.) 



Diaiii. 
ill. 


Cir- 

cunif. 

In. 


Area. 
Sq. In. 


59% 


187.710 


2803.9 


% 


188.103 


2815.7 


60 


188.496 


2827.4 


H 


188.888 


2839.2 




189.281 


2851.0 


'% 


189.674 


2862.9 


V2. 


190.066 


2874.8 


% 


190.459 


2886.6 


% 


190.852 


2898.6 


v% 


191.244 


2910.5 


61 


191.637 


2922.5 


^ 


192.030 


2934.5 


M 


192.423 


2946.5 




192.815 


2958.5 


i 


193.208 


2970.5 


193.601 


2982.7 


% 


193.993 


2994.8 


% 


194.386 


3006.9 


62 


194.779 


3019.1 


^ 


195.171 


3031.3 


M 


195.564 


3043.5 


% 


195.957 


3055.7 




196.3.50 


3068.0 


% 


196.742 


3080.3 


% 


197.135 


3092.6 


% 


197.528 


3104.9 


63 


197.920 


3117 2 


1/^ 


198.313 


3129.6 


M 


198.706 


3142.0 


% 


199.098 


31.54.5 




199.491 


3166.9 


% 


199.881 


3179.4 


H 


200.277 


3191.9 


% 


200.669 


3204.4 


64 


201.062 


3217.0 


% 


201.455 


3229.6 


H 


201.847 


3242.2 


% 


202.240 


3254.8 


6^ 


202.633 


3267.5 




203.025 


3280.1 


M 


203.418 


3292.8 


% 


203.811 


3305.6 


65 


204.204 


3318.3 


/^ 


204.596 


3331.1 


H 


204.989 


3313 9 


% 


205.382 


3356.7 


V'^ 


205.774 


3369.6 


% 


206.167 


3382.4 


% 


206.560 


3395.3 


% 


206.952 


3408.2 


66 


207.345 


3421.2 


/^ 


207.738 


3434.3 


/4 


208.131 


3447.2 


% 


208.-5:^3 


3460.2 


II 


208.916 


3473.2 


209.309 


3486.3 


M 


209.701 


3499.4 


% 


210.094 


3512.5 


67 


210.487 


3525.7 


}^ 


210.879 


3538.8 


^4 


211.272 


3552.0 



Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


67% 


211.665 


3565.2 


1^ 


212.058 


3578.5 


% 


212.450 


3591.7 


SA 


212.843 


3605.0 


% 


213.236 


3618.3 


68 


213.628 


3631.7 




214.021 


3645.0 


M 


214.414 


3658.4 




214 806 


3671.8 


L^ 


215.199 


3685.3 


% 


215.592 


3698.7 


M 


215.984 


371 2. -J 


% 


216.377 


3725.7 


69 


216.770 


3739.3 


Vs 


217.163 


3752. S 


M 


217.555 


3766.4 


% 


217.948 


3780.0 




218.341 


3793.7 


% 


218.733 


3807.3 


•A/ 


219.126 


3821.0 


% 


219.519 


3834.7 


70 


219.911 


3848.5 


H 


220 304 


3862.2 


H 


220.697 


3876.0 




221.090 


3889.8 


L^ 


221.482 


3903.6 


% 


221.875 


3917.5 


M 


222.268 


3931.4 


% 


222.660 


3945.3 


71 


223.053 


3959.2 


Vs 


223.446 


3973.1 


H 


223.838 


3987.1 


% 


224.231 


4001.1 




224.624 


4015.2 


% 


225.017 


4029.2 


% 


225.409 


4043.3 


% 


225.802 


4057.4 


72 


226.195 


4071.5 




226.587 


4085.7 


i 


226.980 


4099.8 


227.373 


4114.0 


i 


227.765 


4128.2 


2:28.158 


4142.5 


M 


228.551 


415e.8 


% 


228.944 


4171.1 


73 


229.336 


4185.4 


H 


229.729 


4199.7 


3^ 


230.122 


4214.1 




230.514 


4228.5 


1^ 


230.907 


4242.9 


&/. 


231.300 


4257.4 


% 


231.692 


4271.8 


% 


232.085 


4286.3 


74 


232.478 


4300.8 


IX 


232.871 


4315.4 


M 


233.263 


4329.9 




233.656 


4344.5 


L^ 


234.049 


4359.2 


% 


^^34.441 


4373.8 


Ps 


234.834 


4388.5 


235.227 


4403 1 



Diana. 
In. 


Cir- 

cumf. 

In. 


75 


235.619 


^ 


236.012 


¥ 


236.405 




236.798 


\4t 


237.190 


% 


237.583 


M 


237.976 


% 


238.368 


76 


2.38.761 


H 


239.154 


M 


239.546 


% 


239.939 




240.332 


% 


240.725 


1 


241.117 


241.510 


77 


241.903 


M 


242.295 


i^ 


242.688 


¥h 


243.081 




243.473 


5^ 


243.866 


H 


244.259 


Vs 


244.6.52 


78 


245.044 


Vs 


245.437 


Va. 


245.830 




246.222 


1^ 


246.615 


Ys 


247.008 


% 


247.400 


% 


247.793 


79 


248.186 




248.579 


^ 


248.971 




249.364 


L^ 


249.757 


% 


250.149 


% 


250.542 


% 


250.935 


80 


251.327 


Vk 


251.720 


H 


252.113 


% 


252.506 




252.898 


% 


253.291 


a^ 


253.684 


% 


254 076 


81 


254.469 


Va 


254.862 


H 


255.254 


H 


255.647 




256.040 


% 


256.433 


H 


256.825 


% 


257.218 


82 


257.611 


% 


258.003 


M 


258.396 


% 


258.789 


^ 


259.181 



MENSURATION. 



415 



AREAS AND CIRCUMFERENCE OF CIRCLES. (Continued.) 



Cir- 

curaf. 

In. 



259.574 
259.967 
260.359 
260.752 
261.145 
261.538 
261.930 
262.:^23 
262.716 
263.108 
263.501 
263.894 
364.286 
264.679 
265.072 
265.465 
265.857 
266.2.50 
266.643 
267.035 
267.428 
267.821 
268.213 
268.606 
268.999 
269.392 
269.784 
270.177 
270.570 
270.962 
271.355 
271.748 
272.140 
272.533 
272.926 
273.319 
273.711 
274.104 
274.497 
274.889 
275.282 
275.675 
276.067 
276.460 
276.853 
277.246 
277.638 



Area. 


Diam. 


Sq. In. 


In. 


5361,8 


88^ 


5378.1 


^ 


5394.3 


M: 


5410.6 


Vs 


5426.9 


89 


5443.3 


Vs 


5459.6 


M 


5476.0 


% 


5492.4 




5508.8 


% 


5525.3 


M 


5541.8 


Vs 


5558.3 


90 


5574.8 




5591.4 


^ 


5607.9 




5624.5 


iz 


5641.2 


% 


5657.8 


n 


5674.5 


Vs 


5691.2 


91 


5707.9 


H 


5724.7 


34 


5741.5 




5758.3 


1/^ 


5775.1 


% 


5791.9 


H 


580H.8 


Vs 


5825.7 


92 


5842.6 


Vs 


5859.6 


H 


58^6.5 


% 


5893.5 




5910.6 


% 


5927.6 


% 


5944.7 


Vs 


.5961.8 


93 


5978.9 


w. 


5996.0 


Vx 


6013.2 




6030.4 


\^ 


6047.6 


% 


6064.9 


•M 


6082.1 


% 


6099.4 


94 


6116.7 


% 


6134.1 


M 



Cir- 

cumf. 

In. 



278.031 
278.424 
278.816 
279.209 
279.602 
279.994 
280.3S7 
280.780 
281.173 
281 .565 
281.9.58 
282.351 
282.743 
283.136 
283.529 
283.921 
284.314 
284 707 
285.100 
285.492 
285.885 
286.278 
286 670 
287.063 
287.456 
287.848 
288.241 
288.634 
289.027 
289.419 
289.812 
290.205 
290.597 
290.990 
291.383 
291.775 
292.168 
292.561 
292.9.54 
293.346 
293.739 
294.132 
294.524 
294.917 
295.310 
295.702 
296.095 



Area. 
Sq. In. 



6151.4 
6168.8 
6186.2 
6203.7 
6221.1 
6238.6 
6256.1 
6273.7 
6291.2 
6308.8 
6326.4 
6344.1 
6361.7 
6379.4 
6397.1 
6414.9 
6432.6 
6450.4 
6468.2 
6486.0 
6503.9 
6521.8 
6539.7 
6.557.6 
6575.5 
6593.5 
6611.5 
6629.6 
6647.6 
6665.7 
6683.8 
6701.9 
6720.1 
6738.2 
6756.4 
6774.7 
6792.9 
6811.2 
6829.5 
6847.8 
6866.1 
6884.5 
6902.9 
6921.3 
6939.8 
6958.2 
6976.7 



Diam. 
In. 


Cir- 

cumf. 

In. 


Area. 
Sq. In. 


94% 


296.488 


6995.3 




296.881 


7013.8 


297.273 


7032.4 


4 


297.666 


7051.0 


Vs 


298.059 


7069.6 


95 


298.451 


7088.2 


Vs 


298.844 


7106.9 


H 


299.237 


7125.6 


% 


299.629 


7144.3 




300.022 


7163.0 


% 


300.415 


7181.8 


H 


300.807 


7200.6 


Vs 


301.200 


7219.4 


96 


301.593 


7238.2 


Vs 


301.986 


7257.1 




302.378 


7276.0 


% 


302.771 


7294.9 


Vq 


303 164 


7313.8 


% 


303.556 


7332.8 


H 


303.949 


7351.8 


Vs 


304.342 


7370.8 


97 


304.734 


7389.8 


Vs 


305.127 


7408.9 


1/4 


305.520 


7428.0 


fs 


305.913 


7447.1 




306.305 


7466.2 


% 


306.698 


7485.3 


% 


307.091 


7.504.5 


Vs 


307.483 


7523.7 


98 


307.876 


7543.0 


% 


308.269 


7562.2 


Va 


308.661 


7581.5 


Vs 


309.054 


7600.8 




309.447 


7620.1 


% 


309.840 


7639.5 


M 


310.232 


7658.9 


Vs 


310.625 


7678.3 


99 


311.018 


7697.7 


Vs 


311.410 


7717.1 


V4 


311.803 


7736.6 


% 


312.196 


7756.1 




312.588 


7775.6 


% 


312.981 


7795.2 


H 


313.374 


7814.8 


Vs 


313.767 


7834.4 


100 


314.159 


7854.0 



416 



MENSUKATIOK. 



Table 82. 
SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


1 


1 


1 


1.0000000 


1.0000000 


1.000000000 


2 


4 


8 


1.4142136 


1.2599210 


.500000000 


3 


9 


27 


1.7320508 


1.4422496 


.333333333 


4 


16 


64 


2.0000000 


1.5874011 


.250000000 


5 


25 


125 


2.2:360680 


1.7099759 


.200000000 


6 


36 


216 


2 4494897 


1.8171206 


.166666667 


7 


49 


343 


2.6457513 


1.9129312 


.142857143 


8 


64 


512 


2.8284271 


2.0000000 


.125000000 


9 


81 


729 


3.0000000 


2.0800837 


.111111111 


10 


100 


1000 


3.1622777 


2.1544347 


.100000000 


11 


121 


1331 


3.3166248 


2.2239801 


.090909091 


12 


144 


1728 


3 4641016 


2.2894286 


.083a33333 


13 


169 


2197 


3.6055513 


2.3513347 


.076923077 


14 


196 


2744 


3.7416574 


2.4101422 


.071428571 


15 


225 


3375 


3.8729833 


2.4662121 


.066666667 


16 


256 


4096 


4.0000000 


2.5198421 


.062500000 


17 


289 


4913 


4.1231056 


2.5712816 


.058823529 


18 


324 


5832 


4.2426407 


2.6207414 


.055555556 


19 


361 


6859 


4.3588989 


2.6684016 


,052631579 


20 


400 


8000 


4.4721360 


2.7144177 


.050000000 


21 


441 


9261 


4.5825757 


2.7589243 


-047619048 


22 


481 


10648 


4.6904158 


2.8020393 


.045454545 


23 


529 


12167 


4.7958315 


2.8438670 


.043478261 


24 


576 


13824 


4.8989795 


2.8844991 


.041666607 


25 


625 


15625 


5.0000000 


2.9240177 


.040000000 


26 


676 


17576 


5.0990195 


2.9624960 


.038461538 


27 


729 


1968:3 


5 1961524 


3.0000000 


.037037037 


28 


784 


21952 


5.2915026 


3.0365889 


.035714286 


29 


841 


24389 


5.3851648 


3.0723168 


.034482759 


30 


900 


27000 


5.4772256 


3.1072325 


.033333333 


31 


961 


29791 


5.5677644 


3.1413806 


.032258065 


32 


1024 


32'^68 


5.6568542 


3.1748021 


.031250000 


33 


1089 


35937 


5.7445626 


3.2075343 


.030303030 


M 


1156 


39304 


5.8309519 


3.2396118 


.029411765 


35 


1225 


42875 


5.9160798 


3.2710663 


.028571429 


36 


1296 


46656 


6.0000000 


3.3019272 


.027777778 


37 


1369 


50653 


6.0827625 


3.832^5^18 


.027027027 


38 


1444 


54872 


6.1644140 


3.3619754 


.026315789 


39 


1521 


59319 


6.2449980 


3.3912114 


.025641026 


40 


1600 


64000 


6.3245553 


3.4199519 


.025000000 


41 


1681 


68921 


6.4031242 


3.4482172 


.024390244 


42 


1764 


74088 


6.4807407 


3.4760266 


.023809524 


43 


1849 


79507 


6.5574385 


3.5033981 


.023255814 


44 


1936 


85184 


6.6332496 


3.5303483 


.022727273 


45 


2025 


91125 


6.7082039 


3.5568933 


.022222222 


46 


2116 


97336 


6.7823300 


3.5830479 


.021739130 


47 


2209 


103823 


6.8556546 


3.6088261 


.021276600 


48 


2304 


110592 


6.9282032 


3.6342411 


.0208:33333 


49 


2401 


117649 


7.0000000 


3.6593057 


.020408163 


50 


2500 


125000 


7.0710678 


3.6840314 


.020000000 


51 


2601 


132651 


7.1414284 


3.7084298 


.019607843 


52 


2704 


140608 


7.2111026 


3.7325111 


.019230769 


53 


2809 


148877 


7.2801099 


3.7562858 


.018867925 


54 


2916 


157464 


7.3484692 


3.7797631 


.Oia5ia519 


55 


3025 


166375 


7.4161985 


3.8029525 


.018181818 


56 


3136 


175616 


7.4833148 


3.8258624 


.017857143 


57 


3249 


185193 


7.5498:344 


3.8485011 


.017543860 


58 


3304 


195112 


7.6157731 


3.8708766 


.017241379 


59 


3481 


205379 


7.6811457 


3.8929965 


.016949153 


60 


3600 


216000 


7.7459667 


3.9148676 


.016666667 


61 


3721 


226981 


7.8102497 


3.0364972 


.016303443 


62 


3844 


238328 


7.8740079 


3.9578915 


.016129032 



MENSURATION. 417 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


63 


3969 


250047 


7.9372539 


3.9790571 


.015873016 


64 


4096 


262144 


8.0000000 


4.0000000 


.015625000 


65 


4225 


274625 


8.0622577 


4.0207256 


.015384615 


66 


4356 


287496 


8.1240384 


4.0412401 


.015151515 


67 


4489 


300763 


8.1853528 


4.0615480 


.014925373 


68 


4624 


314432 


8.2462113 


4.0816551 


.014705882 


69 


4761 


328509 


8.3066239 


4.1015661 


.014492754 


70 


4900 


343000 


8.3666003 


4.1212853 


.014285714 


71 


5041 


357911 


8.4261498 


4.1408178 


.014084507 


72 


5184 


373248 


8.4852814 


4.1601676 


.013888889 


73 


5329 


389017 


8.5440037 


4.1793390 


.013698630 


74 


5476 


405224 


8.6023253 


4.1983364 


.013513514 


75 


5625 


421875 


8.6602540 


4.2171633 


.013333333 


76 


5776 


438976 


8.7177979 


4.2358236 


.013157895 


77 


5929 


456533 


8.7749644 


4.2543210 


.012987013 


78 


6084 


474552 


8.8317609 


4.2725586 


.012820513 


79 


6241 


493039 


8.8881944 


4.2908404 


.012658228 


80 


6400 


512000 


8.9442719 


4.3088695 


.012500000 


81 


6561 


531441 


9.0000000 


4.3267487 


.012345679 


82 


6724 


551368 


9.0553851 


4.3444815 


.012195122 


83 


6889 


571787 


9.1104336 


4.3620707 


.012048193 


84 


7056 


592704 


9.1651514 


4.3795191 


.011904762 


85 


7225 


614125 


9.2195445 


4.3968296 


.011764706 


86 


7396 


636056 


9.2736185 


4.4140049 


.011627907 


87 


7569 


658503 


9.3273791 


4.4310476 


.011494253 


88 


7744 


681472 


9.3808315 


4.4479602 


.011363636 


89 


7921 


704969 


9.4339811 


4.4647451 


.011235955 


90 


8100 


729000 


9.4868330 


4.4814047 


.011111111 


91 


8281 


753571 


9 5393920 


4.4979414 


.010989011 


92 


8464 


778688 


9.5916630 


4.5143574 


.010869565 


93 


8649 


804357 


9.6436508 


4.5306549 


.010752688 


94 


8836 


830584 


9.6953597 


4.5468359 


.010638298 


95 


9025 


857375 


9.7467943 


4.5629026 


.010526316 


96 


9216 


884736 


9.7979590 


4.5788570 


.010416667 


97 


9409 


912673 


9.8488578 


4.5947009 


.010309278 


98 


9604 


941192 


9.8994949 


4.6104363 


.010204082 


99 


9801 


970299 


9.9498744 


4.6260650 


.010101010 


100 


10000 


1000000 


10.0000000 


4.6415888 


.010000000 


101 


10201 


1030301 


10.0498756 


4.6570095 


.009900990 


102 


10404 


1061208 


10.0995049 


4.6723287 


.009803922 


103 


10609 


1092727 


10.1488916 


4.6875482 


.009708738 


104 


10816 


1124864 


10.1980390 


4.7026694 


.009615385 


105 


11025 


1157625 


10.2469508 


4.7176940 


.009523810 


106 


11236 


1191016 


10.2956301 


4.7326235 


.009433962 


107 


11449 


1225043 


10.3440804 


4.7474594 


.009345794 


108 


11664 


1259712 


10.3923048 


4.7622032 


.003259259 


109 


11881 


1295029 


10.4403065 


4.7768562 


.009174312 


110 


12100 


1331000 


10.4880385 


4.7914199 


.009090909 


111 


12321 


1367631 


1015356^8 


4.8058955 


.009009009 


112 


12544 


1404928 


10.5830052 


4.8202845 


.008928571 


113 


12769 


1442897 


10.0801458 


4.8345881 


.008849558 


114 


12996 


1481544 


10.C770783 


4.8488076 


.008771930 


115 


13225 


1520875 


10.7238053 


4.8629442 


.008695652 


116 


13456 


1500896 


10.7703296 


4.8760990 


.008620690 


117 


13689 


1601613 


10.8166538 


4.8909732 


.008547009 


118 


13924 


1643032 


10.8627805 


4.9048681 


.008474576 


119 


14161 


1685159 


10.9087121 


4.9186847 


.008403361 


120 


14400 


1728000 


10.9544512 


4.9324242 


.00838333^1 


121 


14641 


1771561 


11.00)0000 


4.9460874 


^ .00826446. 5 


1^2 


14884 


1815848 


11.0453010 


4.9596757 


.008196721 


123 


15129 


1860867 


11.0905365 


4.9731898 


.00813(K)81 


124 


15376 


1906624 


11.1355287 


4.9866310 


. 00806151 () 



418 



MENSURATION. 



SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued:) 



1 

No. 


Squares. 


Cubes. 


Square 
Roots. 


! 
Cube Roots. 


Reciprocals. 


125 


15625 


1953125 


11.1803399 


5.0000000 


.008000000 


126 


15876 


2000376 


11.2249722 


5.0132979 


.007936508 


127 


16129 


2048383 


11.2694277 


5.0265257 


.007874016 


128 


16384 


2097152 


11.3137085 


5.0396842 


.007812500 


129 


16641 


2146689 


11.3578167 


5.0527743 


.007751938 


130 


16900 


2197000 


11.4017543 


5.0657970 


.007692308 


131 


17161 


2248091 


11.4455231 


5.0787531 


,007633588 


132 


17424 


2299968 


11.4891253 


5.0916434 


.007575758 


133 


17689 


2352637 


11.5325626 


5.1044687 


.007518797 


134 


17956 


2406104 


11.5758369 


5.1172299 


.007462687 


135 


18225 


2460375 


11.6189500 


5.1299278 


.007407407 


136 


18^196 


2515456 


11.6619038 


5.1425632 


.007352941 


137 


18769 


2571353 


11.7046999 


5.1551367 


.007299270 


138 


19044 


2628072 


11.7473401 


5.1676493 


.007^6377 


139 


19321 


2685619 


11.7898261 


5.1801015 


.007194^5 


140 


19600 


2744000 


11.8321596 


6.1924941 


.007142857 


141 


19881 


2803221 


11.8743421 


5.2048279 


.007092199 


142 


20164 


2863288 


11.9163753 


6.2171034 


.007042254 


143 


20449 


29^4207 


11.9582607 


6.2293215 


.006993007 


144 


20736 


2985984 


12.0000000 


5.2414828 


.006944444 


145 


21025 


3048625 


12.0415946 


5.2535879 


.006896552 


146 


21316 


3112136 


12.0830460 


6.2656374 


.006849315 


147 


21609 


3176523 


12.1243557 


5.2776321 


.006802721 


148 


21904 


3241792 


12.1655251 


5.2895725 


.006756757 


149 


22201 


3307949 


12.2065556 


5.3014592 


.006711409 


150 


22500 


3375000 


12.2474487 


5.3132928 


.006666667 


151 


22801 


3442951 


12.2882057 


5.3250740 


.006622517 


152 


23104 


3511808 


12.3288280 


5.3368033 


.006578947 


153 


23409 


3581577 


12.3693169 


5.a484812 


.006535948 


154 


23716 


3652264 


12.4096736 


5.3601084 


.006493506 


155 


24025 


3723875 


12.4498996 


5.3716854 


.006451613 


156 


24336 


3796416 


12.4899960 


5.3832126 


.006410256 


157 


24649 


3869893 


12.5299641 


5 3046907 


.006369427 


158 


24964 


3944312 


12.5698051 


5.4061202 


.006329114 


159 


25281 


4019679 


12.6095202 


5.4175015 


.006289308 


160 


25600 


4096000 


12.6491106 


5.4288352 


.006250000 


161 


25921 


4173281 


12.6885775 


5.4401218 


.C06211180 


162 


26^44 


4251528 


12.7279221 


5.4513618 


.006172840 


163 


26569 


4330747 


12.7671453 


5.4625556 


.006134969 


164 


26896 


4410944 


12.8062485 


5.4737037 


.006097561 


165 


27225 


4492125 


12. 8452326 


5.4848066 


.006060606 


166 


27556 


4574296 


12.8&40987 


5.4058647 


.006024096 


167 


27889 


4657463 


12.9228480 


5.5068784 


.005988024 


168 


28224 


4741632 


12.0614814 


5.5178484 


.005952381 


169 


28561 


4826809 


13.0000000 


5.5287748 


.005917160 


170 


28900 


4913000 


13.0384048 


5.5306583 


.005882353 


171 


29241 


5000211 


13.0766068 


5.5504001 


.00584795:3 


172 


20584 


508&448 


13.1148770 


5.5612078 


.005813953 


173 


29929 


5177717 


13.1520464 


5.5720546 


.005780347 


174 


30276 


5268024 


13.1000060 


5.5827702 


.005747126 


175 


30625 


5350375 


13.2287566 


5.5934447 


.005714286 


176 


30976 


5451776 


13.2664002 


5.6040787 


.005681818 


]77 


31329 


55452a3 


13.3041347 


6.6146724 


.005649718 


178 


316^4 


5639752 


13.3416641 


6.6252263 


.005617978 


179 


32041 


5735339 


13.3790882 


5.6357408 


.005586592 


180 


3^00 


5a32000 


13.4164079 


5.6462162 


.005555.556 


181 


82761 


5920741 


13.4536^0 


5.6566528 


.005524862 


182 


331^ 


6028568 


13.4007:^6 


5.6670511 


.005494505 


183 


a3489 


012ai87 


13.5277493 


5 6774114 


.005464481 


184 


a3856 


6229504 


13.5646600 


5.6877:340 


.0054^478:3 


1H5 


ai225 


63^1625 


13.6014705 


5.6080192 


.005405405 


186 


34596 


64:^856 


13.6381817 


6.7082675 


.005376^44 



MEKSURATTON". 



419 



SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocal. 


187 


34969 


6539203 


13.6747943 


5.7184791 


.005347594 


188 


35344 


6644672 


13.7113092 


5.7286543 


.005319149 


189 


35721 


6751269 


13.7477271 


5.7387936 


.005291005 


190 


36100 


6859000 


13.7840488 


5.7488971 


.005263158 


191 


36481 


6967871 


13.8202750 


5.7589652 


.005235602 


192 


36864 


7077888 


13.8564065 


5.7'689982 


.005208333 


193 


37249 


7189057 


13.8924440 


5.77'89966 


.005181347 


194 


37636 


7301384 


13.9283883 


5.7889604 


.005154639 


195 


38025 


7414875 


13.9642400 


5.7988900 


.005128205 


196 


38416 


7529536 


14.0000000 


5.8087857 


.005102041 


m 


38809 


7645373 


14.0356688 


5.8186479 


.005076142 


198 


39204 


7762392 


14.0712473 


5.8284767 


.005050505 


199 


39601 


7880599 


14.1067360 


5.8382725 


.005025126 


200 


40000 


8000000 


14.1421356 


5.8480355 


.005000000 


201 


40401 


8120601 


14.1774469 


5.8577660 


.004975124 


202 


40804 


8242408 


14.2126704 


5.8674643 


.004950495 


203 


41209 


8365427 


14.2478068 


5.8771307 


.004926108 


204 


41816 


8489664 


14.2828569 


5.8867653 


.004901961 


205 


42025 


8615125 


14.3178211 


5.8963685 


.004878049 


206 


42436 


8741816 


14.3527001 


5.9059406 


.004854369 


207 


42849 


8869743 


14.3874946 


5.9154817 


004830918 


208 


43264 


8998912 


14.4222051 


5.G249921 


.004807692 


209 


43681 


9129329 


14.4568323 


5.9344721 


.004784689 


210 


44100 


9261000 


14.4913767 


5.9439220 


.004761905 


211 


44521 


9393931 


14.5258390 


5.9533418 


.004739336 


212 


44944 


9528128 


14.5602198 


5.9627320 


.004716981 


213 


45369 


9663597 


14.5945195 


5.9720926 


.004694836 


214 


45796 


9800344 


14.6287388 


5.9814240 


.004672897 


215 


46225 


9938375 


14.6628783 


5.9907264 


.004651163 


216 


46656 


10077690 


14.6969385 


6.0000000 


.004629630 


217 


47089 


10218313 


14.7309199 


6.0092450 


.004608295 


218 


47524 


10360232 


14.7648231 


6.0184617 


.004587156 


219 


47961 


10503459 


14.79864S6 


6.0276502 


.004566210 


220 


48400 


10048000 


14.8323970 


6.0368107 


.004545455 


221 


48841 


10793861 


14.8660687 


6.0459435 


.004524887 


222 


49284 


10941048 


14.8996644 


6.0550489 


.004504505 


223 


49729 


11089567 


14.9331845 


6.0641270 


.004484305 


224 


50176 


11239424 


14.9666295 


6.0731779 


.004464286 


225 


50625 


11390625 


15.0000000 


6.0822020 


.004444444 


226 


51076 


11543176 


15.0332964 


6.0911994 


.004424779 


227 


51529 


11697083 


15.0G65192 


6.1001702 


.004405286 


228 


51984 


11852352 


15.0996680 


6.1091147 


.004385965 


229 


52441 


12008989 


15.1327460 


6.1180332 


.004366812 


230 


52900 


12167000 


15.1057509 


6.1269257 


.004347826 


231 


53361 


12326391 


15.1980842 


6.1357924 


.004329004 


232 


53824 


12487168 


15.2315462 


6.1446337 


.004310345 


233 


54289 


12649337 


15.2643375 


6.1534495 


.004291845 


234 


54756 


12812904 


15.2970585 


6.1622401 


.004273504 


235 


55225 


1297787'5 


15.3297'097 


6.1710058 


.004255319 


236 


55696 


13144256 


15.3622915 


6.1797466 


.004237288 


237 


56169 


13312053 


15.3948043 


6.1884628 


.004219409 


238 


56644 


13481272 


15.4272486 


6.1971544 


.004201681 


239 


57121 


13651919 


15.4596248 


6.2058218 


.004184100 


240 


57600 


13824000 


15.4919334 


6.2144650 


.004166667 


241 


58081 


13997521 


15.5241747 


6.2230843 


.004149378 


242 


58564 


14172188 


15.5563492 


6.2316797 


.004132231 


243 


59049 


14M8907 


15.5884573 


6.2402515 


.004115226 


244 


59536 


14526784 


15.6204994 


6.2487998 


.004098361 


245 


60025 


14706125 


15.0524758 


6.2573248 


.004081633 


246 


60516 


14886936 


15.6843871 


6.2658266 


.004065041 


247 


61009 


15069223 


15.71623J36 


6.2743054 


.00404a583 


248 


61504 


15252992 


15.7480157 


6.2827613 


.004032258 



420 MEKSURATIOK. 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


249 


62001 


154382^9 


15.7797338 


6.2911946 


.004016064 


250 


62500 


15625000 


15.81138a3 


6.2996053 


.004000000 


251 


63001 


15813251 


15.8429795 


6.3079935 


.00:3984064 


252 


63504 


16003008 


15.8745079 


6.3163596 


.003968254 


253 


64009 


16194277 


15.9059737 


6.:3247035 


.003952569 


254 


64516 


16:387064 


15.9373775 


6.3330256 


.003937008 


255 


65025 


16581375 


15.9687194 


6.3413257 


.003921569 


256 


65536 


16777216 


16.0000000 


6.3496042 


.003906250 


257 


66049 


16974593 


16.0312195 


6.3578611 


.003891051 


258 


66564 


17173512 


16.0623784 


6.3660968 


.003875969 


259 


67081 


17373979 


16.0934769 


6.3743111 


.00:3861004 


260 


67600 


17576000 


16.1245155 


6.3825043 


.003846154 


261 


68121 


17779581 


16.1554944 


6.3906765 


.003831418 


262 


68644 


17984728 


16.1864141 


6.:3988279 


,003816794 


263 


69169 


18191447 


16.2172747 


6.4069585 


.003802281 


264 


69696 


18399744 


16.2480768 


6.4150687 


.003787879 


265 


70225 


18609625 


16.2788206 


6.4231583 


.003773585 


266 


70756 


18821096 


16.3095064 


6.4312276 


.003759398 


267 


71289 


19034163 


16.3401346 


6.4392767 


.003745318 


268 


71824 


19248832 


16.3707055 


6.4473057 


.003731343 


269 


72361 


19465109 


16.4012195 


6.4553148 


.003717472 


270 


72900 


19683000 


16.4316767 


6.4633041 


.003703704 


271 


73441 


19902511 


16.4620776 


6.4712736 


.003690037 


272 


73984 


20123648 


16.4924225 


6.4792236 


.003676471 


273 


74529 


20346417 


16.5227116 


6.4871541 


.003663004 


274 


75076 


20570824 


16.5529454 


6.4950653 


.003649635 


275 


75625 


20796875 


16.5831240 


6.5029572 


.003636364 


276 


76176 


21024576 


16.6132477 


6.5108300 


.003623188 


277 


76729 


21253933 


16.6433170 


6.5186839 


.003610108 


278 


77284 


21484952 


16.6733320 


6.5265189 


.003597122 


279 


77841 


21717639 


16.7032931 


6 5343351 


.003584229 


280 


78400 


21952000 


16.7332005 


6.5421326 


.003571429 


281 


78961 


22188041 


16.7630546 


6.5499116 


.003558719 


282 


79524 


22425768 


16.7928556 


6.5576722 


.003546099 


283 


80089 


22665187 


16.8226038 


6.5654144 


.003533569 


284 


80656 


22906304 


16.8522995 


6.5731385 


.003521127 


285 


81225 


23149125 


16.8819430 


6.5808443 


.003508772 


286 


81796 


23393656 


16.9115345 


6.5885323 


.003496503 


287 


82369 


23639903 


16.9410743 


6.5962023 


.003484321 


288 


82944 


23887872 


16.9705627 


6.60:38545 


.003472222 


289 


83521 


24137569 


17.0000000 


6.6114890 


.003460208 


290 


84100 


24389000 


17.0293864 


6.6191060 


.003448276 


291 


84681 


24642171 


17.0587221 


6.6267054 


.003436426 


292 


85264 


24897088 


17.0880075 


6.6342874 


.003424658 


293 


85849 


25153757 


17 1172428 


6.6418522 


.003412969 


294 


8G436 


25412184 


17.1464282 


6.6493998 


.003401361 


295 


87025 


25672375 


17.1755640 


6.6569302 


.003389831 


296 


87616 


259343:36 


17.2046505 


6.6644437 


.003378378 


297 


88209 


26198073 


17.2336879 


6.6719403 


.003367003 


298 


88804 


26463593 


17.2626765 


6.6794200 


.003355705 


299 


89401 


26730899 


17.2916165 


6.6868831 


.003344482 


300 


90000 


27000000 


17.3205081 


6.6943295 


.003333333 


301 


90601 


27270901 


17.3493516 


6.7017593 


.003322259 


302 


91204 


27543608 


17.3781472 


6.7091729 


.003311258 


303 


91809 


27818127 


17.4068952 


6.7165700 


.003300330 


304 


92416 


28094464 


17.4355958 


6.7239508 


.003289474 


305 


9.3025 


28:372625 


17.4642192 


6.7313155 


.00:3278689 


306 


93636 


28652616 


17.4928557 


6.7386(>11 


.003267974 


307 


94249 


28934443 


17.5214155 


6.7459967 


.00:3257329 


:m 


94864 


29218112 


17.5499288 


6.7533134 


.003246753 


309 


9M81 


29503(529 


' 17.5783958 


6.7606143 


.003236246 


310 


96100 


29791000 


17.6068169 


6.7678995 


.003225806 



MENSURATIOlsr. 421 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continuec^ .) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


311 


96721 


30080231 


17.6351921 


6.7751690 


.003215434 


312 


97344 


30371328 


17.6685217 


6.7824229 


.003205128 


313 


97969 


30664297 


17.6918060 


6.7896613 


.003194888 


314 


98596 


30959144 


17.7200451 


6.7968844 


.003184713 


315 


99225 


31255875 


17.7482393 


6.8040921 


.003174603 


316 


99856 


31554496 


17.7763888 


6.8112847 


.003164557 


317 


100489 


31855013 


17.8044938 


6.8184620 


.003154574 


318 


101124 


32157432 


17.8325545 


6.8256242 


.003144654 


319 


101761 


32461759 


17.8605711 


6.8327714 


.003134796 


320 


102400 


32768000 


17.8885438 


6.8399037 


.003125000 


321 


103041 


33076161 


17.9164729 


6.8470213 


.003115265 


322 


103684 


33386248 


17.9443584 


6.8541240 


.003105590 


323 


104329 


33698267 


17.9722008 


6.8612120 


.003095975 


324 


104976 


34012224 


18.0000000 


6.8682855 


.003086420 


325 


105625 


34328125 


18.0277564 


6.8753443 


.003076923 


326 


106276 


34645976 


18.0554701 


6.8823888 


.003067485 


327 


106929 


34965783 


18.0831413 


6.8894188 


.003058104 


328 


107584 


35287552 


18.1107703 


6.8964345 


.003048780 


329 


108241 


35611289 


18.1383571 


6.9034359 


.003039514 


330 


108900 


35937000 


18.1659021 


6.9104232 


.003030303 


331 


109561 


36264691 


18.1934054 


6.9173964 


.003021148 


332 


110224 


36594368 


18.2208672 


6.9243556 


.003012048 


333 


110889 


36926037 


18.2482876 


6.9313008 


.003003003 


334 


111556 


37259704 


18.2756669 


6.9382321 


.002994012 


335 


112225 


37595375 


18.3030052 


6.9451496 


.002985075 


336 


112896 


37933056 


18.3303028 


6.9520533 


.002976190 


337 


113569 


38272753 


18.3575598 


6.9589434 


.002967359 


338 


114244 


38614472 


18.3847763 


6,9658198 


.002958580 


339 


114921 


38958219 


18.4119526 


6.9726826 


.002949853 


340 


115600 


39304000 


18.4390889 


6.9795321 


.002941176 


341 


116281 


39651821 


18.4661853 


6.9863681 


.002932551 


342 


116964 


40001688 


18.4932420 


6.9931906 


.002923977 


343 


117649 


40353607 


18.5202592 


7.0000000 


.002915452 


344 


118336 


40707584 


18.5472370 


7.0067962 


.002906977 


345 


119025 


41063625 


18.5741756 


7 0135791 


,002898551 


346 


119716 


41421736 


18.6010752 


7.0203490 


.002890173 


347 


120409 


41781923 


18.6279360 


7.0271058 


.002881844 


348 


121104 


42144192 


18.6547581 


7.0338497 


.002873563 


349 


121801 


42508549 


18.6815417 


7.0405806 


.002865330 


350 


122500 


42875000 


18.7082869 


7.0472987 


.002857143 


351 


123201 


43243551 


18.7349940 


7.0540041 


.002849003 


352 


123904 


43614208 


18.7616630 


7.0606967 


.002840909 


353 


124609 


43986977 


18.7882942 


7.0673767 


.002832861 


354 


125316 


44361864 


18.8148877 


7.0740440 


.002824859 


355 


126025 


44738875 


18.8414437 


7.0806988 


.002816901 


356 


126736 


45118016 


18.8679623 


7.0873411 


.002808989 


357 


127449 


45499293 


18.8944436 


7.0939709 


.002801120 


358 


128164 


45882712 


18.9208879 


7.1005885 


.002793296 


359 


128881 


46268279 


18.9472953 


7.1071937 


.002785515 


360 


129600 


46656000 


18.9736660 


7.1137866 


.002777778 


361 


130321 


47045881 


19.0000000 


7.1203674 


.002770083 


362 


131044 


47437928 


19.0262976 


7.1269360 


.002762431 


363 


131769 


47832147 


19.0525589 


7.1334925 


.002754821 


364 


132496 


48228544 


19.0787840 


7.1400370 


.00274725;^ 


365 


133225 


48627125 


19.1049732 


7.1465695 


.002739726 


366 


133956 


49027'896 


19.1311265 


7.1530901 


.002732240 


367 


134689 


49430863 


19.1572441 


7.1595988 


.002724796 


368 


135424 


49836032 


19.1833261 


7.1660957 


.002717391 


369 


136161 


50243409 


19.2093727 


7.1725809 


.002710027 


370 


136900 


50653000 


19.2353841 


7.1790544 


002702703 


371 


137641 


51061811 


19.2613603 


7.1H551()2 


.002r)95tl8 


372 


138384 


51478848 


19.2873015 


7.1919663 


.002688172 



422 MENSURATIOK". 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


373 


139129 


51895117 


19.3132079 


7.1984050 


.002680965 


374 


139876 


52313624 


19.3390796 


7.2048322 


.002673797 


375 


140625 


52734375 


19.3649167 


7.2112479 


.002666667 


376 


141376 


53157376 


19.3907194 


7.2176522 


.002659574 


377 


142129 


53582633 


19.4164878 


7.2240450 


.002652520 


378 


142884 


54010152 


19.4422221 


7.2304268 


.002645503 


379 


143641 


54439939 


19.4679223 


7.2367972 


.002638522 


380 


144400 


54872000 


19.4935887 


7.2431565 


.002631579 


381 


145161 


55306341 


19.5192213 


7.2495045 


.002624672 


382 


145924 


55742968 


19.5448203 


7.2558415 


.002617801 


383 


146689 


56181887 


19.5703858 


7.2621675 


.002610966 


384 


147456 


56623104 


19.5959179 


7.2684824 


.002604167 


385 


148225 


57066625 


19.6214169 


7.2747864 


.002597403 


386 


148996 


5751^56 


19.6468827 


7.2810794 


.002590674 


387 


149769 


57960603 


19.6723156 


7.2873617 


.002583979 


388 


150544 


58411072 


19.6977156 


7.2936330 


.002577320 


389 


151321 


58863869 


19.7230829 


7.2998936 


.002570694 


390 


152100 


59319000 


19.7484177 


7.3061436 


.002564103 


391 


152881 


59776471 


19.7737199 


7.3123828 


.002557545 


392 


153664 


602&6288 


19.7989899 


7.3186114 


.002551020 


393 


154449 


60698457 


19.824^276 


7.3248295 


.002544529 


394 


155236 


61162984 


19.8494332 


7.3310369 


.002538071 


395 


156025 


61629875 


19.8746069 


7.3372339 


.002531646 


396 


156816 


62099136 


19.8997487 


7.3434205 


.002525253 


397 


157609 


62570773 


19.9248588 


7.3495966 


.002518892 


398 


158404 


63044792 


19.9499373 


7.3557624 


.002512563 


399 


159201 


63521199 


19.9749844 


7.3619178 


.002506266 


400 


160000 


64000000 


20.0000000 


7.3680630 


.002500000 


401 


160801 


64481201 


20.0249844 


7.3741979 


.002493766 


402 


161604 


64964808 


20.0499377 


7.3803227 


.002487562 


403 


162409 


65450827 


20.0748599 


7.3864373 


.002481390 


404 


163216 


65939264 


20.0997512 


7.3925418 


.002475248 


405 


164025 


66430125 


20.1246118 


7.3986363 


.002469136 


406 


164836 


66923416 


20.1494417 


7.4047206 


.002463054 


407 


165649 


67419143 


20.1742410 


7.4107950 


.002457002 


408 


166464 


67917312 


20.1990099 


7.4168595 


.002450980 


409 


167281 


08417929 


20.2237484 


7.4229142 


.002444988 


410 


168100 


68921000 


20.2484567 


7.4289589 


.0024390^ 


411 


168921 


69426531 


20.2731349 


7.4349938 


.002433090 


412 


169744 


69934528 


20.2977831 


7.4410189 


.002427184 


413 


170569 


70444997 


20.3224014 


7.4470342 


.002421308 


414 


171396 


70957944 


20.3469899 


7.4530:399 


.002415459 


415 


172225 


71473375 


20.3715488 


7.4590359 


.002409639 


416 


173056 


71991296 


20.3960781 


7.4650223 


.002403846 


417 


173889 


72511713 


20.4205779 


7.4709991 


.002398082 


418 


174724 


73034032 


20.4450483 


7.4769664 


.002392344 


419 


175561 


73560059 


20.4694895 


7.4829242 


.002386635 


420 


176400 


74088000 


20.4939015 


7.4888724 


.002380952 


421 


177241 


74618461 


20.5182845 


7.4948113 


.002375297 


422 


178084 


75151448 


20.5426386 


7.5007406 


.002369668 


423 


178929 


•i5686967 


20.5669638 


7.5066607 


.002364066 


4^ 


179776 


;6225024 


20 5912603 


7.5125715 


.002358491 


425 


180625 


76765625 


20.6155281 


7.5184730 


.002352941 


426 


181476 


77308776 


20.6397674 


7.52^13652 


.002^7418 


427 


182329 


77854483 


20.66397^3 


7.5302482 


.002341920 


428 


183184 


78^02752 


20.6881609 


7.5361221 


.002336440 


429 


184041 


7895:3589 


20.712:3152 


7.5419867 


.002331002 


430 


184000 


70507000 


20.7364414 


7.5478423 


.002325581 


431 


1H.-)761 


8(K)I)2991 


20.7005395 


7.5536888 


.002320186 


432 


1866i^4 


80621568 


20.7846097 


7.5595263 


.002314815 


433 


187489 


81182737 


20.8086520 


7.5053548 


.002309469 


431 


18H356 


81746504 


20.8326667 


7.5711743 


.002:304147 



MENSURATTOK. 



423 



SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 















No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


435 


189225 


82312875 


20.8566536 


7.5769849 


.002298851 


436 


190096 


82881856 


20.8806130 


7.5827865 


.002293578 


437 


190969 


83453453 


20.9045450 


7.5885793 


.002288330 


438 


191844 


84027672 


20.9284495 


7.5943633 


.002283105 


439 


192721 


84604519 


20.9523268 


7.6001385 


.002277904 


440 


193600 


85184000 


20.9761770 


7.6059049 


.002272727 


441 


194481 


85766121 


21.0000000 


7.6116626 


.002267574 


442 


195364 


86350888 


21.0237960 


7.6174116 


.002262443 


413 


196249 


86938307 


21.0475652 


7.6231519 


.002257336 


444 


197136 


87528384 


21.0713075 


7.6288837 


.002252252 


415 


198025 


88121125 


21.0950231 


7.6346067 


.002247191 


416 


198916 


88716536 


21.1187121 


7.6403213 


.002242152 


447 


199809 


89314623 


21.1423745 


7.6460272 


.002237136 


448 


200704 


89915392 


21.1660105 


7.6517247 


.002232143 


449 


201601 


90518849 


21.1896201 


7.6574138 


.002227171 


450 


202500 


91125000 


21.2132034 
21.2367606 


7.6630943 


.002222222 


451 


203401 


91733351 


7.0687665 


.002217295 


452 


204304 


92345408 


21.2602916 


7.6744303 


.002212389 


453 


205209 


92959677 


21.2837967 


7.6800857 


.002207506 


454 


206116 


93576664 


21.3072758 


7.6857328 


.002202643 


455 


207025 


94196375 


21.3307290 


7.6913717 


.002197802 


456 


207936 


94818816 


21.3541565 


7.6970023 


.002192982 


457 


208849 


95443993 


21.3775583 


7.7026246 


.002188184 


458 


209764 


96071912 


21.4009346 


7.7082388 


.002183406 


459 


210681 


96702579 


21.4242853 


7.7138448 


.002178649 


460 


211600 


97336000 


21.4476106 


7.7194426 


.002173913 


461 


212521 


97972181 


21.4709106 


7.7'250325 


.002169197 


462 


213444 


08611128 


21.4941853 


7.7306141 


.C02164502 


463 


214369 


99252847 


21.5174348 


7. 7361877 


.002159827 


464 


215296 


99897344 


21.5406592 


7.7417532 


.002155172 


465 


216225 


100544625 


21.5638587 


7.7473109 


.002150533 


466 


217156 


101194696 


21.5870331 


7.7528606 


.002145923 


467 


218089 


101847563 


21.6101828 


7.7584023 


.002141328 


468 


219024 


102503232 


21.6333077 


7.7639361 


.002136752 


469 


219961 


103161709 


21.6564078 


7.7694620 


.00213219G 


470 


220900 


103823000 


21.6794834 


7.7749801 


.002127660 


471 


221841 


104487111 


21.7025a44 


7.7-804904 


.002123142 


472 


222784 


105154048 


21.7255610 


7.7859928 


.002118644 


473 


223729 


105823817 


21.7485632 


7.7914875 


.002114165 


474 


224676 


106496424 


21.7715411 


7.7969745 


.002109705 


475 


225625 


107171875 


21.7944947 


7.8024538 


.002105263 


476 


226576 


107850176 


21.8174242 


7.8079254 


.002100840 


477 


227529 


108531333 


21.8403297 


7.8133892 


.002096436 


478 


228484 


109215352 


21 8632111 


7.8188456 


.002092050 


479 


229441 


109902239 


21.8860686 


7.8242942 


.002087-683 


480 


230400 


110592000 


21.9089023 


7.8297'353 


.002088333 


481 


231361 


111284641 


21.9317122 


7.8351688 


.002079002 


482 


232324 


111980168 


21.9544984 


7.8405949 


.00207-4689 


483 


233289 


112678587 


21.9772610 


7.8460134 


.00207-0393 


484 


234256 


113379904 


22.0000000 


7.8514244 


.002066116 


485 


235225 


114084125 


22.0227155 


7.8568281 


.002061856 


486 


236196 


114791256 


22.0454077 


7.8622242 


.002057613 


487 


237169 


115501303 


22.0680765 


7.8676130 


.002051^88 


488 


238144 


116214272 


22.0907220 


7.8729944 


.002049180 


489 


239121 


116930169 


22.1133444 


7 87^3684 


.00204-1990 


490 


240100 


117649000 


22.1359436 


7.8837352 


.002040810 


491 


241081 


118370771 


22.1585198 


7.8890946 


.00203()660 


492 


242064 


119095488 


22.1810730 


7.8944468 


.002032520 


493 


243049 


119823157 


22.2036033 


7.8997917 


.0Ou)283S)8 


494 


244036 


12()5537K4 


22.2261108 


7.9051294 


.(X 12024291 


495 


245025 


121287375 


22.2485955 


7.91(M599 


.(K)2020202 


496 


246016 


122023930 


22.2710575 


7.9157832 


.002016129 



424 



MENSURATIOlSr. 



SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


497 


247009 


122763473 


22.2934968 


7.9210994 


.002012072 


498 


248004 


12:3,505992 


22.3159136 


7.9264085 


.002008032 


499 


249001 


124251499 


22.3383079 


7.9317104 


.002004008 


500 


250000 


125000000 


22.3606798 


7.9370053 


.002000000 


501 


251001 


125751501 


22.3830293 


7.9422931 


.001996008 


502 


252J04 


126506008 


22.4053565 


7.9475739 


.001992032 


503 


253009 


127263527 


22.4276615 


7.952^477 


.001988072 


504 


254016 


128024064 


22.4499443 


7.9581144 


.0019&4127 


505 


255025 


128787625 


22.4722051 


7.9^33743 


.001980198 


506 


256036 


1295M216 


22.4944438 


7.9686271 


.001976285 


507 


257049 


130323&43 


22.5166605 


7.9738731 


.001972:387 


508 


258064 


131096512 


22.5388553 


7.9791122 


.00196a5O4 


509 


259081 


131872229 


22.5610283 


7.9843444 


.0019&4637 


510 


260100 


132651000 


22.5831796 


7.9895697 


.001960784 


511 


261121 


133432831 


22.6053091 


7.9947883 


.001956947 


512 


262144 


134217728 


22.6274170 


8.0000000 


.001953125 


513 


263169 


1:35005697 


22.6495033 


8.0052049 


.001949:318 


514 


264196 


135796744 


22.6715681 


8.0104032 


.001945525 


515 


265225 


136590875 


22.6936114 


8.0155946 


.001941748 


516 


266256 


137388096 


22.7156334 


8.0207794 


.001937984 


517 


267289 


1381-88413 


22.7376340 


8.0259574 


.0019.34236 


518 


268324 


1:38991832 


22.7596134 


8.0311287 


.0019.30502 


519 


269361 


139798359 


22.7815715 


8.0362935 


.001926782 


520 


270400 


140608000 


22.803,5085 


8.0414.515 


.001923077 


521 


271441 


141420761 


22.8254244 


8.0466030 


.001919380 


522 


272484 


142236648 


22.8473193 


8.0517479 


.001915709 


523 


273529 


143055667 


22.8691933 


8.0568862 


.001912046 


524 


274576 


143877824 


22.8910463 


8.0620180 


.001908397 


525 


275625 


144703125 


22.9128785 


8.0671432 


.001904762 


526 


276676 


145531576 


22.9:346899 


8.0722620 


.001901141 


527 


277729 


146363183 


22.9564806 


8.0773743 


.001897533 


528 


278784 


147197952 


22.9782506 


8.0824800 


.00189:39:39 


529 


279841 


148035889 


23.0000000 


8.0875794 


.001890359 


530 


280900 


148877000 


23.0217289 


8.0926723 


.001886792 


531 


281961 


149721291 


23.04.34:372 


8.0977589 


.001883239 


532 


283024 


150.568768 


23.0651252 


8.1028390 


.001879699 


5^3 


2^4089 


151419437 


23.0867928 


8.1079128 


.001876173 


534 


285156 


152273304 


23.1084400 


8.1129803 


.G018T2659 


535 


286225 


153130375 


23.1:300670 


8.1180414 


.001869150 


536 


287296 


153990656 


23.1,5167:38 


8.1230962 


.001865672 


537 


288369 


1548M153 


23.1732605 


8.1281447 


.001862197 


538 


289444 


155720872 


2:3.1048270 


8.1.3.31870 


.00ia5873G 


539 


290521 


156590819 


23.2163735 


8.1382230 


.001855288 


540 


291600 


157464000 


23.2379001 


8.1432529 


.001851852 


5-11 


292681 


1.58340421 


23 2594067 


8.1482765 


.00ia4&423 


542 


293764 


159220088 


23.28089:35 


8.1532939 


.001^45018 


543 


294'^9 


16C103007 


23.302.3604 


8.1583051 


.001841621 


544 


295936 


160989184 


23.3238076 


8.1633102 


.0018382:35 


545 


297025 


161878625 


23.3452:351 


8.1683092 


.0018.34862 


546 


298116 


162771336 


23.3666429 


8.1733020 


.0018:31502 


547 


290209 


16366732:3 


23. 3880.311 


8.1782888 


.001828154 


548 


300304 


164566.502 


23.4003098 


8. 1^32695 


.001824813 


549 


301401 


165469149 


23.4307490 


8.1882441 


.001821494 


550 


302.500 


166375000 


23.45207f:8 


8.1932127 


.C018181C? 


551 


303601 


167JS41.-:i 


£3,47.33802 


8.1981753 


.001814882 


552 


304704 


168196608 


23.4946802 


8.20.31319 


.001811594 


553 


30.5809 


169112377 


23.51.59.520 


8.2080825 


.001808318 


554 


306016 


170031464 


23.. 5.372046 


8.21:30271 


.001805054 


555 


308025 


17095:3875 


23. 5,5^4,380 


8.2179657 


.001801802 


5.56 


300136 


171879616 


23., 5796.522 


8.2«28985 


.001798561 


557 


310219 


172808693 


23.600a474 


8.2278254 


.00179.5332 


558 


311364 


173741112 


23.6220236 


8.2327463 


.001792115 



MEKSURATION. 425 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


559 


312481 


174676879 


23.6431808 


8.2376614 


.001788909 1 


560 


313600 


175616000 


23.6643191 


8.2425706 


.001785714 


561 


314721 


176558481 


23.6854386 


8.2474740 


.001782531 


562 


315844 


177504328 


23.7065392 


8.2523715 


,001779359 i 


563 


316969 


178453547 


23.7276210 


8.2572633 


.001776199 


564 


318096 


179406144 


23.7486842 


8.2621492 


.001773050 


565 


319225 


180362125 


23.7697286 


8.2670294 


.001769912 


566 


320356 


181321496 


23.7907545 


8.2719039 


.001766784 


567 


321489 


182284263 


23.8117618 


8.2767726 


,001763668 


568 


322624 


183250432 


23.8327506 


8.2816355 


.001760563 


669 


323761 


184220000 


J>3.8537209 


8.2864928 


.001757469 


570 


324900 


185193000 


23.8746728 


8.2913444 


.001754386 


571 


326041 


186169411 


23.8956063 


8.2961903 


.001751313 


572 


327184 


187149248 


23.9165215 


8.3010304 


.001748252 


573 


328329 


188132517 


23.9374184 


8.3058651 


.001745201 


574 


329476 


189119224 


23.9582971 


8.3106941 


.001742160 


575 


330625 


190109375 


23.9791576 


8.3155175 


.001739130 


576 


331776 


191102976 


24.0000000 


8.3203353 


.001736111 


577 


332929 


192100033 


24.0208243 


8.3251475 


.001733102 


578 


334084 


193100552 


24.0416306 


8.3299542 


.001730104 


579 


335241 


194104539 


24.0624188 


8.3347553 


.001727116 


580 


336400 


195112000 


24.0831891 


8.3395509 


.001724138 


581 


337561 


196122941 


24.1039416 


8.3443410 


.001721170 


582 


338724 


197137368 


24.12467G2 


8.3491256 


.001718213 


583 


339889 


198155287 


24.1453929 


8.3539047 


.001715266 


584 


341056 


199176704 


24.1660919 


8.3586784 


.001712329 


585 


342225 


200201625 


24.1867732 


8.3634466 


.001709402 


586 


a43396 


201230056 


24.2074369 


8.3682095 


.001706485 


587 


344569 


202262003 


24.2280829 


8.3729668 


.001703578 


588 


345744 


203297472 


24.2487113 


8.3777188 


001700680 


589 


346921 


204336469 


24.26932^2 


8.382465a 


001697793 


590 


348100 


205379000 


24.2899156 


8.3872065 


.001694915 


591 


349281 


206425071 


2-1.3104916 


8.3919423 


.001692047 


592 


350464 


207474688 


24.3310501 


8.3966729 


.001689189 


593 


351649 


208527857 


24.3515913 


8.4013981 


.001686341 


594 


352836 


209584584 


24.3721152 


8.4061180 


.001683502 


595 


354025 


210644875 


24.3926218 


8.4108326 


-001680672 


596 


355216 


211708736 


24.4131112 


8.4155419 


.001677852 


597 


356409 


212776173 


24.4335^34 


8.4202460 


.001675042 


598 


357604 


213847192 


24.4540385 


8.4249448 


.001672241 


599 


358801 


214921799 


24.4744765 


8.4296383 


.001669449 


600 


360000 


216000000 


24.4948974 


8.4348267 


.001666667 


601 


361201 


217081801 


24.51.53013 


8.4390098 


.001668894 


602 


362404 


218167208 


24.5356883 


8.4436877 


.001661130 


603 


363609 


219256227 


24.5560583 


8.4483605 


.001658375 


604 


364816 


220348864 


24.5764115 


8.4530281 


.001655629 


605 


366025 


221445125 


24.5967478 


8.4576906 


.001652893 


606 


367236 


222545016 


24.6170673 


8.4623479 


.001650165 


607 


368449 


223648543 


24.6373700 


8.4670001 


.001647446 


608 


369664 


224755712 


24.6576560 


8.4716471 


.001644737 


609 


370881 


225866529 


24.6779254 


8.4762892 


.001642036 


610 


372100 


226981000 


24.6981781 


8.4800261 


.001639344 


611 


373321 


228099131 


24.7184142 


8.4855579 


.001636661 


612 


374544 


229220928 


24.7386338 


8.4901848 


..001633987 


613 


375769 


230346307 


24.7588368 


8.4948065 


.001631321 


614 


370996 


231475544 


24.7790234 


8.4994233 


.001628664 


615 


378225 


232008375 


24.7'991935 


8.5040350 


.001626016 


616 


379456 


233744896 


24.8193473 


8.n086417 


.001623377 


617 


380689 


234885113 


24.8394847 


8.5132435 


.001620746 


618 


381924 


236029032 


24.8596058 


8.5178403 


.001618123 


619 


383161 


237176659 


»4. 87971 06 


8.522^4321 


.001615509 


620 


384400 


238328000 


2^1.8997992 


8.5270189 


.001612903 



426 ME:^SUliATION. 

SQUARE ROOTS AND CUBE ROOTS OF NUriBERS. 



(Continued.) 





Ko. 


Sr-uares 


1 

Cubes 

1 


Square 
Roots. 


Cabe RooLs. 


Reciprocals. 




621 


385641 


239483061 


24.9198716 


8.. 5316009 


.001610306 




622 


i 386884 


240tKH848 


24.9399278 


8.5361780 


.001607717 




G23 


388129 


241804367 


24.9599679 


8.5407501 


.001605136 




G24 


389376 


242970624 


24.9799920 


8.5453173 


.001602564 




625 


390625 


244140625 


25.0000000 


8.5498797 


.001600000 




626 


391876 


245314376 


25.0199920 


8.0544372 


.001597444 




627 


393129 


24049188:3 


25.0399681 


8.5589899 


.001594896 




628 


394384 


247'673152 


25.0599282 


8.56.35377 


.001592357 




629 


395641 


248858189 


25.0798724 


8.5680807 


.001589825 




630 


396900 


250047000 


25.0998008 


8.5726189 


.001587302 




631 


398161 


251239591 


25.1197134 


8.. 5771523 


.0015^786 




632 


399424 


252435968 


25.1396102 


8.5816809 


.001582278 




633 


400689 


253636137 


25.1594913 


8.5862047 


.001579779 




634 


401956 


254840104 


25.1793566 


8.5907238 


.001577287 




635 


403225 


256047875 


25.1992063 


8.5952380 


.001574803 




636 


404496 


257259456 


25.2190404 


8.5997476 


.001572327 




637 


405769 


2,58474853 


25.2388589 


8.6042525 


.001569859 




638 


407044 


239694072 


25.2586619 


8.6087526 


001567398 




639 


408321 


260917119 


25.2784493 


8.6132480 


.001564945 




640 


409600 


262144000 


25.2982213 


8.6177388 


.001562500 




641 


410881 


263374721 


25. 31 79778 


8.6222248 


.001560062 




642 


412164 


264609288 


25.3377189 


8.6267063 


.0015576.32 




643 


413449 


265847707 


25.3574447 


8.6311830 


.001.555210 




644 


414736 


267089984 


25.3771551 


8.6356551 


.001552795 




645 


416025 


268336125 


25.3968502 


8.6401226 


.001550388 




646 


417316 


269586136 


25.4165.301 


8.6445855 


.001547988 




647 


418609 


270840023 


25.4361947 


8.&490437 


.001545595 




648 


419904 


2720977'92 


25.4558441 


8.6534974 


.00154:3210 




649 


421201 


273359449 


25.4754784 


8.6579465 


.001540832 




650 


422500 


274625000 


25.49.50976 


8.6623911 


.001,5.38462 




651 


423801 


275894451 


25.5147016 


8.6668310 


.0015.36098 




652 


425104 


277167808 


25.5a42907 


8.6712665 


.001.533742 




653 


426409 


278445077 


25.5538647 


8.6756974 


.001531.394 




654 


427716 


279726264 


25.57^4237 


8.6801237 


.001529052 




655 


429025 


281011375 


25.5929678 


8.6845456 


.001526718 




656 


430336 


282300416 


25.6124969 


8.6889630 


.001524390 




657 


431649 


283593393 


25.6320112 


8.69:33759 


.001522070 




658 


432964 


284890312 


25.6515107 


8.6977843 


.001519757 




659 


434281 


286191179 


25.6709953 


8.7021882 


.001517451 




660 


4a5600 


287496000 


25.6904652 


8.7065877 


.00151.5152 




661 


436921 


288804781 


25.7099203 


8.7109827 


.001512859 




662 


438244 


290117528 


25.7293607 


8.715.3734 


.001510574 




663 


439569 


2914.34247 


25.7487864 


8.7197596 


.001508296 




664 


440896 


292754944 


25.7681975 


8.7241414 


.001506024 




665 


442225 


294079625 


25.7875939 


8.7285187 


.001503759 




666 


44.3.556 


29.5408296 


25.8069758 


8.7328918 


.001501502 




667 


444889 


296740963 


25.826.3431 


8.7372604 


.001499250 




668 


446224 


2980776.32 


25.84.56960 


8.7416246 


.001497006 




669 


447561 


2994ia309 


25.8650.343 


8.7459846 


.001494768 




670 


448900 


30076.3000 


25.884.3.582 


8.7.50.3401 


.0014925.37 




671 


450241 


302111711 


25.9036677 


8.7.546913 


.001490313 




672 


451584 


30.3464448 


25.9229628 


8.7590383 


.001488095 




673 


452929 


304821217 


25.94224.35 


8.76.33809 


.0014a5884 




674 


4.54276 


300182024 


25.961.5100 


8.7677192 


.00148:3680 




675 


4.55625 


307546875 


25.9807621 


8.7720532 


.001481481 




676 


4.56976 


308915776 


26.0000000 


8.776.38.30 


.001479290 




677 


458329 


31028873:^ 


26.01922.37 


8.7807084 


.001477105 




678 


459684 


31166.5752 


26.0.-384.331 


8.78,50296 


.001474926 




679 


461041 


3Ki046839 


26.0576284 


8.7893466 


.00147-2754 




680 


462400 


3144.32000 


26.0768096 


8.79.36.593 


.001470588 




681 


463761 


31.5821241 


26.0959767 


8.7979679 


.001468429 




682 


465124 


317214568 


26.1151297 1 


8.8022721 1 


.001466276 



MEKSURATIOK. 



427 



SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



1 

i No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


G83 


466489 


318611987 


26.1342687 


8 8065722 


.001464120 


684 


467856 


320013504 


26.1533937 


8.8108681 


.001461988 


685 


469225 


321419125 


26.1725047 


8.8151598 


.001459854 


686 


470596 


322828856 


26.1916017 


8.8194474 


.001457726 


687 


471969 


324242703 


26.2106848 


8.8237307 


.001455604 


688 


473344 


325660672 


26.2297541 


8.8280099 


.001453488 


689 


4747'21 


327082769 


26.2488095 


8.8322850 


.001451379 


690 


476100 


328509000 


26.2678511 


8.8365559 


.001449275 


691 


477481 


329939371 


26.2868789 


8.8408227 


.001447178 


692 


478864 


331373888 


26.3058929 


8.8450854 


.001445087 


693 


480249 


332812557 


26.3248932 


8.8493440 


.001443001 


694 


481636 


334255384 


26.3438797 


8.8535985 


.001440922 


695 


483025 


335702375 


26.3628527 


8.8578489 


.001438849 


696 


484416 


337158536 


26.3818119 


8.8620952 


.001436782 


697 


485809 


338608873 


26.4007576 


8.866337'5 


.001434720 


698 


487204 


340068392 


26.4196896 


8.8705757 


.001432665 


699 


488601 


341532099 


26.4386081 


8.8748099 


.001430615 


700 


490000 


.343000000 


26.4575131 


8.8790400 


.001428571 


701 


491401 


344472101 


26.4764046 


8.8832661 


.001426534 


702 


492804 


345948408 


26.4952826 


8.8874882 


.001424501 


703 


494209 


347428927 


26.5141472 


8.8917063 


.001422475 


704 


495616 


348913664 


26.5329983 


8.8959204 


.001420455 


.705 


497025 


350402625 


26.5518361 


8.9001304 


.001418440 


706 


498436 


351895816 


26.5706605 


8.9043366 


.001416431 


707 


499849 


353393243 


26.5894716 


8.9085387 


.001414427 


708 


501264 


354894912 


26.6082694 


8.9127369 


.001412429 


709 


502681 


356400829 


26 6270539 


8.9169311 


.001410437 


710 


504100 


357911000 


26.6458252 


8.9211214 


.001408451 


711 


505521 


359425431 


26.6645833 


8.9253078 


.001406470 


712 


506944 


360944128 


26.6833281 


8.9294902 


.001404494 


713 


508369 


362467097 


26.7020598 


8.9336687 


.001402525 


714 


509796 


363994344 


26.72077'84 


8.9378433 


.001400560 


715 


511225 


365525875 


26.7394839 


8.9420140 


.001398601 


716 


512656 


367061696 


26.7581763 


8.9461809 


.001396648 


717 


514089 


368601813 


26.7768557 


8.9503438 


.001394700 


718 


515524 


370146232 


26.7955220 


8.9545029 


.001392758 


719 


516961 


371694959 


26.8141754 


8.9586581 


.001390821 


720 


518400 


373248000 


26.8328157 


8.9628095 


,001388889 


721 


519841 


374805361 


26.8514432 


8.9669570 


.001386963 


722 


521284 


376367048 


26.870057r 


8.9711007 


.001385042 


723 


522729 


377933067 


26.8886593 


8.9752406 


.001383126 


724 


524176 


379503424 


26.9072481 


8.9793766 


.001381215 


725 


525625 


381078125 


26.9258240 


8.9835089 


.001379310 


726 


527076 


382657176 


26.9443872 


8.9876373 


.001377410 


727 


528529 


384240583 


26.9629375 


8.9917620 


.001375516 


728 


529984 


385828352 


26.9814751 


8.9958829 


.001373626 


729 


531441 


387'420489 


27.0000000 


9.0000000 


.001371742 


730 


532900 


389017000 


27.0185122 


9.0041134 


.001369863 


731 


534361 


39061 7891 


27.0370117 


9.0082229 


.001367989 


732 


535824 


392223168 


27.0554985 


9.0123288 


.001366120 


733 


537289 


393832837 


27.0739727 


9.0164309 


.001364256 


734 


538756 


395446904 


27.0924344 


9.0205293 


.001362398 


735 


540225 


397005375 


27.1108834 


9.0246239 


.001360544 


736 


541696 


398088256 


27.1293199 


9.0287149 


.001358696 


737 


543169 


400315553 


27.1477439 


9.0328021 


.00135(5852 


738 


544644 


401947272 


27.1661554 


9.0368857 


.001355014 


739 


540121 


403583419 


27.1845544 


9.0409655 


.001353180 


740 


547600 


405224000 


27.2029410 


9 0450419 


.001351351 


741 


549081 


4068<)9021 


27.2213152 


9.0491112 


.001349528 


742 


550564 


408518488 


27.2396769 


fV 0531 831 


.0013 1770;) 


743 


552049 


410172107 


27.2580263 j 


i>. 0572182 


,0l)134r)H9r) 


744 


553536 


411830784 


27.27'63634 | 


9.0613098 


.001314086 



428 



MENSURATION. 



SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


745 


555025 


4ia493625 


27.2946881 


9.065.3677 


.001:^2282 


746 


556516 


4151609:36 


27.:3130006 


9.0694>?3 


.001:^048:3 


747 


558009 


4168:3272:3 


27.3:31:3007 


9.07^726 


.001:3:38688 


748 


559504 


418508992 


27.^49.5887 


9.0775197 


.001336898 


749 


561001 


420189749 


27.3678644 


9.0815031 


.001335113 


750 


562.500 


421875000 


27.3861279 


9. 0656030 


.001333333 


751 


5^001 


42:3564751 


27.4043792 


9.0896392 


.0(.1331558 


752 


565504 


425259008 


27.4226184 


9.0936719 


.001329787 


753 


567009 


426957777 


27.4408455 


9.0977010 


.001328021 


754 


568516 


428661064 


27.4590604 


9.1017265 


.001326260 


755 


570O35 


4:30368875 


27.4772633 


9.1057485 


.001324503 


756 


5715:36 


4:32081216 


27.4954542 


9.1097669 


.001322751 


757 


57:3049 


4:3:3798093 


27.51363:30 


9.1137818 


.001321004 


758 


574564 


4:35519512 


27.5:317998 


9.1177931 


.001:319261 


759 


576081 


4:37245479 


27.5499546 


9.1218010 


.001317523 


760 


577600 


438976000 


27.5680975 


9.1258053 


.001315789 


761 


579121 


440711081 


27.5862284 


9.1298061 


.001:314060 


762 


580<>44 


442450728 


27.6043475 


9.1338034 


.001:312336 


763 


582169 


444194947 


27.62-:4546 


9.1377971 


.001310616 


764 


58:3696 


445943744 


27.6405499 


9.1417874 


.001:308901 


765 


585225 


447697125 


27.6586:3^4 


9.1457742 


.001:30719(3 


766 


586756 


4494.55096 


27.6767050 


9.1497576 


.001:30548:3 


767 


588289 


45121766:3 


27.6947648 


9.1537^75 


.001:303781 


768 


589824 


4529848:32 


27.7128129 


9.15771:39 


.001:30208:3. 


769 


591:361 


454756609 


27.7308492 


9.1616869 


.001:300390 


rro 


592900 


4565a3000 


27.74887:39 


9.1656565 


.001298701 


7n 


594441 


458314011 


27.7668868 


9.1696225 


.001297017 


772 


595984 


460099648 


27.7848880 


9.1735852 


.001295337 


773 


597529 


461889917 


27.8028775 


9.1775445 


.001293661 


774 


599076 


46:3684824 


27.8208555 


9.1815003 


.001291990 


775 


600625 


465484:375 


27.8:388218 


9.1854527 


.001290323 


776 


602176 


467288576 


27.8567766 


9.18^018 


.001288660 


777 


603729 


4690974:3:3 


27.8747197 


9.193.S474 


.0)1287001 


TTS 


605284 


470910952 


27.8926514 


9.1972897 


.001285^47 


779 


606841 


472729139 


27.9105715 


9.2012286 


.001283697 


780 


60^100 


474552000 


27.92S4801 


9.2051641 


.001282051 


781 


609961 


476379541 


27.946:3772 


9-2090962 


.001280410 


782 


611524 


478211768 


27.9042629 


9 2130250 


.001,2'iK7V2 


783 


61:3089 


480048687 


27.9821:372 


9.2169505 


.0012771:39 


784 


614656 


481890:304 


28.0000000 


9.220e?26 


.001275510 


785 


616225 


483?36625 


28.0178515 


9.2247914 


.00127:3885 


7^ 


617796 


485587656 


28.0356915 


9.2287068 


.001272265 


787 


619:369 


48744:^403 


28.05:35203 


9.2326189 


.001270048 


788 


620944 


489:303872 


28.0713:377 


9.2365277 


.001269036 


789 


622521 


491169069 


28.0891438 


9.2404333 


.001267427 


790 


624100 


4930:39000 


28.1069.386 


9.^443355 


.001265823 


791 


625681 


494913671 


28.1247222 


9.2482:^44 


.001204223 


792 


627^ 


49679:3088 


28.1424946 


9.2521300 


.001262626 


793 


628^9 


498677257 


28.1602557 


9.2560224 


.0012610^4 


794 


6304:36 


500566184 


28.1780056 


9.2599114 


.001259446 


795 


632025 


502459875 


28.1957444 


9.2637973 


,001257862 


796 


63:3616 


504:358:336 


28.21:^4720 


9.2676798 


.0012.56281 


797 


6:35209 


50626157:3 


28.2:3118}i4 


9.2715592 


.00l::54705 


798 


636804 


508169592 


28.24889:38 


9.2754352 


.001253133 


799 


63^^01 


510082399 


28.2665881 


9.2793061 


.001251504 


800 


6400<X) 


512000000 


28.2842712 


9.2831777 


.001250000 


801 


t>41601 


513922401 


28.:3011M:^ 


9.2870440 


.001248439 


802 


&43204 


515H49608 


28. :3196045 


9.2909072 


.00124688:3 


803 


644809 


517781627 


28:3:372546 


9.2^76n 


.001245330 


804 


64&416 


51971S4W 


28. :35489:38 


9.29862:39 


.00124:3781 


806 


648025 


521W)0125 


28.:3725219 


9.3^^4775 


.001242236 


806 


W9636 


52:3606616 


28.:390i:391 


9.3063278 


.001240695 



MENSURATIOJSr. 429 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. (Continued,) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


807 


651249 


525557943 


28.4077454 


9.3101750 


.001239157 


808 


652864 


527514112 


28.4253408 


9.3140190 


.001237624 


809 


654481 


529475129 


28.4429253 


9.3178599 


.001236094 


810 


656100 


531441000 


28.4604989 


9.3216975 


.001234568 


811 


657721 


533411731 


28.4780617 


9.3255320 


.001233046 


812 


659344 


535387328 


28.4956137 


9.3293634 


.001231527 


813 


660969 


537367797 


28.5131549 


9.3331916 


.001230012 


814 


662596 


539353144 


28.5306852 


9.3370167 


.001228501 


815 


664225 


541343375 


28.5482048 


9.3408386 


.001226994 


816 


665856 


543336496 


28.5657137 


9.3446575 


.001225490 


817 


667489 


545338513 


28.5832119 


9.3484731 


.001223990 


818 


669124 


547343432 


28.6006993 


9.3522857 


.001222494 


819 


670761 


549353259 


28.6181760 


9.3560952 


.001221001 


820 


672400 


551368000 


28.6356421 


9.3599016 


.001219512 


821 


674041 


553387661 


28.6530976 


9.3637049 


.001218027 


822 


675684 


555412248 


28.6705424 


9.3675051 


.001216545 


823 


677329 


557441767 


28.6879766 


9.3713022 


.001215067 


824 


678976 


559476224 


28.7054002 


9.3750963 


.001213592 


825 


680625 


561515625 


28.7228132 


9.3788873 


.001212121 


826 


682276 


563559976 


28.7402157 


9.3826752 


.001210654 


827 


683929 


565609283 


28.7576077 


9.3864600 


.001209190 


828 


685584 


567663552 


28.7749891 


9.3902419 


.001207729 


829 


687'241 


569722789 


28.7923601 


9.3940206 


.001206273 


830 


688900 


571787000 


28.8097206 


9.3977964 


.001204819 


831 


690561 


573856191 


28.82707'06 


9.4015691 


.001203369 


832 


692224 


575930368 


28.8444102 


9.4053387 


.001201923 


833 


693889 


578009537 


28.8617394 


9.4091054 


.001200480 


834 


695556 


580093704 


28.8790582 


9.4128690 


.001199041 


835 


697225 


582182875 


28.8963666 


9.4166297 


.001197605 


836 


698896 


584277056 


28.9136646 


9.4203873 


.001196172 


837 


700569 


586376253 


28.9309523 


9.4241420 


.001194743 


838 


702244 


588480472 


28.9482297 


9.4278936 


.001193317 


839 


703921 


590589719 


28.9654967 


9.4316423 


.001191895 


840 


705600 


592704000 


28.9827535 


9.4353880 


.001190476 


841 


707281 


594823321 


29.0000000 


9.4391307 


.001189061 


842 


708964 


596947688 


29.0172363 


9.4428704 


.001187648 


843 


710649 


599077107 


29.0344623 


9.4466072 


.001186240 


844 


712336 


601211584 


29.0516781 


9.4503-410 


.001184834 


845 


714025 


603351125 


29.0688837 


9.4540719 


.001183432 


846 


715716 


605495736 


29.0860791 


9.4577999 


.001182033 


847 


717409 


607645423 


29.1032644 


9.4615249 


.001180638 


848 


719104 


609800192 


29.1204396 


9.4652470 


.001179245 


849 


720801 


611960049 


29.1376046 


9.4689661 


.001177856 


850 


722500 


614125000 


29.1547595 


9.4726824 


.001176471 


851 


724201 


616295051 


29.1719043 


9.4763957 


.001175088 


852 


725904 


618470208 


29.1890390 


9.4801061 


.001173709 


853 


727609 


620650477 


29.2061637 


9.4838136 


.001172333 


854 


729316 


622835804 


29.2232784 


9.4875182 


.001170960 


855 


731025 


62502G87'5 


29.2403830 


9.4912200 


.001169591 


856 


732736 


627222016 


29.2574777 


9.4919188 


.001168224 


857 


7;i4449 


629422793 


29.2745623 


9.4986147 


.00116(5861 


858 


7'3()164 


631628712 


29.2916370 


9.5023078 


.0011(55501 


859 


737881 


6338397. 9 


29.3087018 


9.5059980 


.001164144 


860 


739600 


636056000 


29.3257566 


9.5096854 


.001162791 


861 


741321 


638277381 


29.3128015 


9.5K^3699 


.0011(51440 


862 


74^3044 


640503928 


29.35983(55 


9.5170515 


.0011()(X)93 


863 


744769 


642735647 


29.3768616 


9.5207303 


.(K)l 158749 


864 


746496 


644972544 


29.3938769 


9.52440(53 


.001157407 


865 


748225 


647214625 


29.410S82:3 


9.5280794 


.00115(5069 


866 


749956 


649461896 


29.4278779 


9.5317497 


.001154?34 


867 


7'51689 


651714363 


29.4448637 


9.5354172 


.001153403 


868 


75134^ 


653972032 


29.4618397 


9.5390818 


,001152074 



430 



MENSURATION. 



SQUARE ROOTS 


AND CUBE 


ROOTS OF NUMBERS. (Continued.) 


Ko. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


ReciprocaISi 


869 


755161 


6562:34909 


29.4788059 


9.5427437 


.001150748 


870 


756900 


^58,503000 


29.4957624 


9.5464027 


.001149425 


871 


758641 


660776.311 


29.5127091 


9.. 5500589 


.001148106 


872 


7a'):384 


60:3054848 


29.529»>461 


9.55:37123 


.001146789 


873 


762129 


665:3.38617 


29.54657:34 


9.5573630 


.00114,5475 


874 


763876 


667627624 


29.56:34910 


, 9.5610108 


.001144165 


875 


765625 


669921875 


29.580:3989 


9.5646559 


.001142857 


876 


767376 


672221376 


29.5972972 


9.5682982 


.001141553 


877 


769129 


67452613:3 


29.6141858 


9.5719377 


.001140^1 


878 


770884 


6768:36152 


29. mums 


9.5755745 


.001138952 


879 


772641 


679151439 


29.6479342 


9.5792085 


.001137656 


880 


774400 


' 681472000 


29.6647939 


9.5828397 


.001136364 


881 


776161 


683797841 


29.6:?16442 


9.5864682 


.001135074 


882 


777924 


686128968 


29.69t>4848 


9.59<J0939 


.0011:33787 


.t«3 


779689 


688465387 


29.7153159 


9.5937169 


.001132503 


88i 


781456 


690807104 


29.7:321375 


9.5973373 


.0011:31222 


885 


78:3.225 


693154125 


29.7489496 


9.6009548 


.001129944 


886 


784996 


695506456 


29.7657521 


9.6045696 


.001128668 


887 


786769 


697864103 


29.7825452 


9.6081817 


.001127:396 


888 


788544 


700227072 


29.799:3289 


: 9.6117911 


.001126126 


889 


790321 


702595369 


29.8161030 


1 9.6153977 


.001124859 


890 


792100 


704969000 


29.8328678 


1 9.6190017 


.001123596 


891 


793881 


707:347971 


29.8496231 


1 9.6226030 


.001122334 


892 


795664 


709732288 


29.866:3690 


i 9.6262016 


.001121076 


893 


797449 


712121957 


29.88:31056 


; 9.6297975 


.001119821 


894 


799236 


714516984 


29.8998328 


i 9.6333907 


.001118568 


895 


801025 


716917375 


29.9165506 


i 9.6369812 


.001117318 


896 


802816 


71932:3136 


29.9:332591 


i 9.6405690 


.001116071 


897 


804609 


7217:^73 


29.9499583 


; 9.6441542 


.001114827 


898 


806404 


7241.50792 


29.9666481 


1 9.6477367 


.001113586 


899 


808201 


726572699 


29.98:33287 


9.6513166 


.001112^47 


900 


810000 


729000000 


30.0000000 


9.6548938 


.001111111 


901 


811801 


731432701 


30.0166620 


9.6584684 


.001109878 


902 


813604 


7a3870808 


dO.(mS148 


9.6620403 


.001108647 


903 


815409 


736314.327 


30.0499584 


9.66,5a")96 


.001107420 


904 


817216 


738763264 


30.0665928 


9.6691762 


.0011G6195 


905 


819025 


741217625 


30.0832179 


9.6727403 


.001104972 


906 


820836 


74:3677416 


30.0998:339 


9.676:3017 


.001ia3753 


907 


822649 


746142643 


30.1164407 


9.6798604 


.001102,536 


908 


8^4464 


748613312 


30.1:3:30:38:3 


9.68^4166 


.001101322 


909 


826281 


751089429 


30.1496269 


9.6869701 


.001100110 


910 


828100 


753571000 


30.1662063 


9.6905211 


.001098901 


911 


829921 


7560580:31 


30.1827765 


9.6940694 


.001097695 


912 


831744 


758550528 


30.199:3377 


9.6976151 


.00109^91 


913 


833569 


761048497 


30.2158899 


9.7011583 


.001095290 


914 


835396 


76:3551944 


30.2:324:329 


9.7046989 


.001094092 


915 


8:37225 


7660()0875 


30.2489669 


9.7082369 


.00l092}ip6 
.001091TO3 


916 


839056 


76857.5296 


30.26.54919 


9.7117723 


917 


8408S9 


771095213 


30.2<v.>0()79 


9.7153051 


.001090513 


918 


842724 


773620632 


30.298,5148 


9.7188354 


.001089:335 


919 


844561 


776151559 


30.3150128 


9.722:3631 


.001088139 


920 


84^00 


778688000 


30.3315018 


9.72,58883 


.001086957 


921 


848^1 


781229961 


30.;3479818 


9.7294109 


.001085776 


922 


R500H4 


78:3777448 


30.3644.529 


9.7329309 


.001084599 


923 


851 929 


786:3:3(^167 


30.38091.51 


9.7364484 


00108.3423 


924 


K53776 


7.SS8>^'»024 


30.. 397:36,^3 


9.7:3996.^4 


.001082251 


925 


8.5.562,5 


7914.5:3125 


30.41:38127 


9.74^47.58 


.001081081 


926 


857476 


794(h22776 


30.4:3(.>2481 


9.7469^57 


.001079914 


927 


859.32<i 


7i«;5979K3 


30.4-166747 


9.7,5049:30 


.001078749 


928 


8^31184 


79917S7.52 


30.46:3(MfcM 


9.75:39979 


.001077586 


929 


8<>3041 


80l7(xi089 


30.4795013 


9.7575002 


.001076426 


930 


8G4900 


804357000 


30.4959014 


9.7610001 


.001075269 



MENSURATION. 431 

SQUARE ROurS AND CUBE ROOTS OF NUMBERS. {Continued.) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


931 


866761 


806954491 


30.5122926 


9.7644974 


.001074114 


932 


868624 


809557568 


30.5286750 


9.7679922 


.001072961 


933 


870489 


812166237 


30,5450487 


9.7714845 


.001071811 


934 


872356 


814780504 


30.5614136 


9.7749743 


-001070664 


935 


874225 


817400375 


30.5777697 


9.7784616 


.001069519 


936 


876096 


820025856 


30.5941171 


9.7819466 


.001068376 


937 


877969 


822656953 


30.6104557 


9.7854288 


.001067236 


938 


879844 


825293672 


30.6267857 


9.78S9087 


.001066098 


939 


881721 


827936019 


30.6431069 


9.7923861 


,001064963 


940 


883600 


830584000 


30.6594194 


9.7958611 


.001063830 


941 


885481 


833237621 


30.6757233 


9,7993336 


.001062699 


942 


887364 


835896888 


30.6920ia5 


9.8028036 


.001061571 


943 


889249 


838561807 


30.7083051 


9.8062711 


.001060445 


944 


891136 


841232384 


30.7'245830 


9.8097362 


.001059322 


945 


893025 


843908625 


30.7'408523 


9.8131989 


.001058201 


946 


894916 


846590536 


30.7571130 


9.8166591 


.001057082 


947 


896809 


849278123 


30.7733651 


9.8201169 


.001055966 


948 


898704 


851971392 


30.7896086 


9.8235723 


.001054852 


949 


900601 


854670349 


30.8058436 


9.8270252 


.001053741 


950 


902500 


857375000 


30.8220700 


9.8304757 


.001052632 


951 


904401 


860085351 


30.8382879 


9.8339238 


.001051525 


952 


906304 


862801408 


30.8544972 


9. 8373695 


-001050420 


953 


908209 


865523177 


30.8706981 


9.8408127 


. 001049318 


954 


910116 


868250664 


30.8868904 


9.8442536 


.001048218 


955 


912025 


870983875 


30.9030743 


9.8476920 


.001047120 


956 


913936 


873722816 


30.9192497 


9.8511280 


.0010460^5 


557 


915849 


876467493 


30.9354166 


9.8545617 


.001044932 


D58 


917764 


879217912 


30.9515751 


9.8579929 


.001043841 


S59 


919681 


881974079 


30.9677251 


9.8614218 


.001042753 


S60 


921600 


884736000 


30.9838668 


9.8648483 


.001041667 


J)61 


923521 


887503681 


31.0000000 


9.8682724 


.001040583 


S62 


925444 


890277128 


31.0161248 


9.8716941 


.001039501 


963 


927369 


893056347 


31.0322413 


9.8751135 


.001038422 


S64 


929296 


895841344 


31.0483494 


9.8785305 


.001037344 


965 


931225 


898632125 


31.0644491 


9.8819451 


.001036269 


966 


933156 


901428696 


31.0805405 


9.885357'4 


.001035197 


967 


935089 


904231063 


31.0966236 


9.8887673 


.001034126 


968 


937024 


907039232 


31.1126984 


9.8921749 


.001038058 


969 


938961 


909853209 


31.1287648 


9.8955801 


.001031992 


970 


940900 


912673000 


31.1448230 


e. 8989830 


.001030928 


971 


942841 


915498611 


31.1608729 


9.9023835 


.001029866 


972 


944784 


918330048 


31.1769145 


9.9057817 


.001028807 


973 


946729 


921167317 


31.1929479 


9.9091776 


.001027749 


974 


948676 


924010424 


31.2089731 


9.9125712 


.001026694 


975 


950625 


926859375 


31.2249900 


9.9159624 


.001025641 


976 


952576 


929714176 


31.2409987 


9.9193513 


.001024590 


977 


954529 


932574833 


31.2569992 


9.9227379 


.001023541 


978 


956484 


935441352 


31.2729915 


9.9261222 


.001022495 


979 


958441 


938313739 


31.2889757 


9.9295042 


.001021450 


980 


960400 


941192000 


31.3049517 


9.9328839 


.001020408 


981 


962361 


94407()141 


31.3209195 


9.9362613 


.001019368 


982 


904324 


946966168 


31.3368792 


9.9396363 


.001018330 


983 


966289 


949862087 


31.3528308 


9.9430092 


.001017294 


984 


968256 


952763904 


31. 3687743 


9.9463797 


.001016260 


985 


970225 


955671625 


31.3847097 


9.9497479 


.001015228 


986 


972196 


958585256 


31.4006369 


9.9531138 


.001014199 


987 


974169 


961504803 


31.4165561 


9.95(54775 


.001013171 


988 


976144 


964430272 


31.4324673 


9.95981^9 


.001012146 


989 


978121 


967361669 


31.4483704 


9.9631981 


.001011122 


990 


980100 


970299000 


31,4642654 


9.9665549 


.001010101 


991 


982081 


973242271 


31.4801525 


9.9699095 


.001009082 


993 


9S4064 


976191488 


81.4960315 


9.9732619 


.001008065 



432 MENSURATION. 

SQUARE ROOTS AND CUBE ROOTS OF NUMBERS. {^Continued,) 



No. 


Squares. 


Cubes. 


Square 
Roots. 


Cube Roots. 


Reciprocals. 


993 


986049 


979146657 


31.5119025 


9.9766120 


.001007049 


994 


988036 


982107784 


31.5277655 


9.9799599 


.001006036 


995 


990025 


985074875 


31.5436206 


9.9833055 


.001005025 


996 


992016 


988047936 


31.5594677 


9.9866488 


.001004016 


997 


994009 


991026973 


31.5753068 


9.9899900 


.001003009 


998 


996004 


994011992 


31.5911380 


9.9933289 


.001002004 


999 


998001 


997002999 


31.6069613 


9.9966656 


.001001001 


1000 


1000000 


1000000000 


31.6227766 


10.0000000 


.001000000 


1001 


1002001 


1003003001 


31.6385840 


10.0033322 


.0009990010 


1002 


1004004 


1006012008 


31.6543836 


10.0066622 


.0009980040 


1003 


1006009 


1009027027 


31.6701752 


10-0099899 


.0009970090 


1004 


1008016 


1012)48064 


31.6859590 


10.0133155 


.0009960159 


1005 


1010025 


1015075125 


31.7017349 


10.0166389 


.0009950249 


1006 


1012036 


1018108216 


31.7175030 


10=0199601 


.0009940358 


1007 


1014049 


1021147343 


31.7332633 


10.0232791 


.0009930487 


1008 


1016064 


1024192512 


31.7490157 


10.0265958 


.0009920635 


1009 


1018081 


1027243729 


31.7647603 


10.0299104 


.0009910803 


1010 


1020100 


1030301000 


31.7804972 


10.0332228 


.0009900990 


1011 


1022121 


1033364331 


31.7962262 


10.0365330 


.0009891197 


1012 


1024144 


1036433728 


31.8119474 


10.0398410 


.0009881423 


1013 


1026169 


1039509197 


31.8276609 


10.0431469 


.0009871668 


1014 


1028196 


1042590744 


31.8433666 


10.0464506 


.0009861933 


1015 


1030225 


1045678375 


31.8590646 


10.0497521 


.0009852217 


1016 


1032256 


1048772096 


31.8747549 


10.0530514 


.0009842520 


1017 


1034289 


1051871913 


31.8904374 


10.0563485 


.0009832842 


1018 


1036324 


1054977832 


31.9061123 


10.0596435 


.0009823183 


1019 


1038361 


1058089859 


31.9217794 


10.0629364 


.0009813543 


1020 


1040400 


1061208000 


31.9374388 


10.0662271 


.0009803922 


1021 


1042441 


1064332261 


31.9530906 


10. 0695156 


.0009794319 


1022 


1044484 


1067462648 


31.9687347 


10.0728020 


.0009784736 


1023 


1046529 


1070599167 


31.9843712 


10.0760863 


.0009775171 


1024 


1048576 


1073741824 


32.0000000 


10.0793684 


.0009765625 


1025 


1050665 


10r6890625 


32.0156212 


10.0826484 


.0009756098 


1026 


1052676 


1080045576 


32.0312348 


10.0859262 


.0009746589 


1027 


1054729 


1083206683 


32.0468407 


10 0892019 


.0009737098 


iae8 


1056784 


1036373952 


32.0624391 


10.09247.55 


.0009727626 


1029 


1058841 


1039547389 


32.0780298 


10.0957469 


.0009718173 


1030 


1060900 


1092727000 


32.0936131 


10.0990163 


.0009708738 


1031 


1062961 


1095912791 


32.1091887 


10.1022835 


.0009699321 


1032 


1065024 


1099104768 


3S. 1247568 


10.1055487 


.0009689922 


1033 


1067089 


1102302937 


32.1403173 


10.1088117 


.0009680542 


1034 


1069156 


1105507304 


32.1558704 


10.1120726 


.0009671180 


1035 


1071225 


1108717875 


32.1714159 


10.1153314 


.0009661836 


1036 


1073296 


1111934656 


32.1869539 


10.118.5882 


.0009652510 


1037 


1075369 


1115157653 


32.2024844 


10.1218428 


.0009643202 


1038 


1077444 


1118386872 


32.2180074 


10.1250953 


.0009633911 


1039 


1079521 


1121622319 


32.2335229 


10 .1283457 


.0009624639 


1040 


1081600 


1124864000 


32.2490310 


10.1315941 


.0009615385 


1041 


1083681 


1128111921 


32.26453116 


10.1348403 


.0009606148 


1042 


1085764 


1131366088 


32.2800^48 


10.1380845 


.0009596929 


1043 


1087849 


1134626507 


32.2955105 


10.1413266 


.0009587738 


1044 


1089936 


1137893184 


32.3109888 


10-1445667 


.0009578544 


1045 


1092025 


1141166125 


32.3264598 


10 1478047 


.0009569378 


1046 


1094116 


1144445336 


32.3419233 


10 1510406 


.0009560229 


1047 


1096209 


1147730823 


32.a573794 


10 1542744 


.0009551098 


1048 


1098304 


1151022592 


32.3728281 


10.1575062 


.0009541985 


1049 


1100401 


1154320649 


32.3882695 


10.1607359 


.0009532888 


1050 


1102500 


1157625000 


32.4037035 


10.1639636 


.0009523810 


1051 


1 1104601 


1160935651 


32.41M301 


10.1671893 


.0009514748 


10.52 


1106704 


1164252608 


32.4345495 


10.1704129 


.0009505703 


1053 


1108809 


1167575877 


32 4499615 


10.1736344 


.0009496676 


1054 


1110916 


1170905464 


32.4653662 


10.1768539 


.0009487666 



Table 83. 

LOGARITHMS OF NUMBERS 

PROM 

1 to 10,000 
TO SIX DECIMAL PLACES. 



N. 


Log. 


N. 


Log. 1 


N. 


Log. 


N. 


Log. 


N. 


Log. 


1 


0.000000 


21 


1.322219 


41 


1.612784 


61 


1.785330 


SI 


1.908485 


2 


0.301030 


22 


1.342423 j 


42 


1.623249 


62 


1.792392 


82 


1.913814 


3 


0.477121 


23 


1.361728 


43 


1.633468 


63 


1.799341 


83 


1.919078 


4 


0.602060 


24 


1.380211 


44 


1.643453 


64 


1.806180 


84 


1.924279 


5 


0.698970 


25 


1.397940 : 


45 


1.653213 


65 


1.812913 


85 


1.929419 


6 


0.778151 


26 


1.414973 


46 


1.662758 


66 


1.819544 


86 


1.934498 


7 


0.845098 


27 


1.431364 


47 


1.672098 


67 


1.826075 


87 


1.939519 


8 


0.903090 


28 


1.447158 


48 


1.681241 


68 


1.832509 


88 


1.944483 


9 


0.954243 


29 


1.462398 


49 


1.690196 


69 


1.838849 


89 


1.949390 


10 


1.000000 


30 


1.477121 


50 


1.698970 


70 


1.845098 


90 


1.954243 


11 


1.041393 


31 


1.491362 


51 


1.707570 


71 


1.851258 


91 


1.959041 


12 


1.079181 


32 


1.505150 


52 


1.716003 


72 


1.857332 


92 


1.963788 


13 


1.113943 


33 


1.518514 


53 


1.724276 


73 


1.863323 


93 


1.968483 


14 


1.146128 


34 


1.531479 


54 


1.732394 


74 


1.869232 


94 


1.973128 


15 


1.176091 


35 


1.544068 


55 


1.740363 


75 


1.875061 


95 


1.977724 


16 


1 204120 


36 


1.556303 


56 


1.748188 


76 


1.880814 


96 


1.982271 


17 


1.2304i9 


37 


1.568202 


57 


1.755875 


77 


1.886491 


97 


1.986772 


18 


1.255273 


38 


1.579784 


58 


1.763428 


78 


1.892095 


98 


1.991226 


19 


1.278754 


39 


1.591065 


59 


1.770852 


79 


1.897627. 


99 


1.995035 


20 


1.301030 


40 


1.602060 


60 


1.778151 


80 


1.903090 


100 


2.000000 



483 



434 



LOGARTTTTMS OF NUMBl^RS. 



No. 100 L. 000.1 



r.No. 109 L. 040. 



N. 





1 


2 


8 


4 


100 
1 
2 


000000 
4321 
8600 


0434 
4751 
9026 


0868 
5181 
9451 


1301 
5609 
9876 


1734 
6038 


0300 
4521 
8700 


3 

4 


012837 
7033 


3259 
7451 


3680 
7868 


4100 

82^4 


5 
6 

7 


021189 
5306 
93^ 


1603 
5715 
9789 


2016 
6125 


2428 
6533 


2841 
6942 


0195 
4227 
8223 


0600 
4628 
8620 


1004 
5029 
9017 


8 
9 


033424 
7426 
04 


3826 
7825 



2166 
^66 


2598 
6894 


3029 
7821 


0724 
4940 
9116 


1147 
5360 
9532 


1570 
5779 
9947 


3252 
7350 


3664 


4075 
8164 



3461 3891 
7748 8174 



1993 2415 
6197 6616 



0361 0775 

4486 

8571 



1408 ! 1812 2216 
5430 5830 6230 

9414 9811 

I 0207 



2619 
6629 



3021 
7028 



0602 I 0998 



Diff. 



432 

426 

424 

420 

416 
412 
408 

404 

400 

397 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


434 


43.4 1 


86.8 


130.2 


173.6 


217.0 


260.4 


303.8 


a47.2 


390.6 


433 


43.3 ; 


86.6 


129.9 


173.2 


216.5 


259.8 


303.1 


346.4 


389.7 


432 


43.2 


86.4 


129.6 


172.8 


216.0 


259.2 


302.4 


345.6 


388.8 


431 


43.1 


86.2 


129.3 


172.4 


215.5 


258.6 


301.7 


344.8 


387.9 


430 


43.0 


86.0 


129.0 


172.0 


215.0 


258.0 


301.0 


344.0 


387.0 


429 


42.9 


85.8 


128.7 


171.6 


214.5 


257.4 


300.3 


a43.2 


386.1 


428 


42.8 


85.6 


128.4 


171.2 


214.0 


256.8 


299.6 


342.4 


385.2 


427 


42.7 


85.4 


128.1 


170.8 


213.5 


256.2 


298.9 


341.6 


384.3 


426 


42.6 


85.2 


127.8 


170.4 


213.0 


255.6 


29S.2 


340.8 


383.4 


425 


42.5 


85.0 


127.5 


170.0 


212.5 


255.0 


297.5 


340.0 


382.5 


424 


42.4 


84.8 


127.2 


169.6 


212.0 


254.4 


296.8 


339.2 


381.6 


423 


42.3 


84.6 


126.9 


169.2 


211.5 


253.8 


296.1 


338.4 


380.7 


422 


42.2 


84.4 


126.6 


168.8 


211.0 


253.2 


295.4 


337.6 


379.8 


421 


42.1 


84.2 


126.3 


168.4 


210.5 


252.6 


294.7 


336.8 


378.9 


420 


42.0 


&4.0 


126.0 


168.0 


210.0 


252.0 


294.0 


336.0 


378.0 


419 


41.9 


83.8 


125.7 


167.6 


209.5 


251.4 


293.3 


335.2 


377.1 


418 


1 41.8 


83.6 


125.4 


167.2 


209.0 


250.8 


292.6 


334.4 


376.2 


417 


; 41.7 


8:3.4 


125.1 


166.8 


208.5 


250.2 


291.9 


333.6 


375.3 


416 


41.6 


83.2 


1^.8 


166.4 


208.0 


249.6 


291.2 


332.8 


374.4 


415 


41.5 


853.0 


124.5 


166.0 


207.5 


249.0 


290.5 


332.0 


373.5 


414 


! 41.4 


82.8 


124.2 


165.6 


207.0 


248.4 


289.8 


331.2 


372.6 


413 


i 41.3 


82.6 


123.9 


165.2 


206.5 


247.8 


289.1 


330.4 


371.7 


412 


1 41.2 


82.4 


123.6 


164.8 


206.0 


247.2 


288.4 


329.6 


370.8 


411 


1 41.1 


82.2 


123.3 


164.4 


205.5 


^6.6 


287.7 


328.8 


369.9 


410 


' 41.0 


82.0 


123.0 


164.0 


205.0 


246.0 


287.0 


328.0 


309.0 


409 


1 40.9 


81.8 


122.7 


163.6 


204.5 


245.4 


286.3 


327.2 


368.1 


408 


1 40 8 


81.6 


122.4 


163.2 


! 204.0 


244.8 


285.6 


326.4 


367.2 


407 


i 40.7 


81.4 


122.1 


162.8 


: 203.5 


^44. 2 


284.9 


325.6 


366.3 


406 


1 40.6 


81.2 


121.8 


162.4 


20:3.0 


243 6 


284.2 


324.8 


365.4 


405 


1 40.5 


81.0 


121.5 


162.0 


202.5 


243.0 


283.5 


324.0 


364.5 


404 


1 40.4 


80.8 


121.2 


161.6 


202.0 


! 242.4 


282.8 


323.2 


363.6 


403 


1 40.3 


80.6 


120.9 


161.2 


201.5 


241.8 


282.1 


322.4 


362.7 


402 


1 40.2 


80.4 


120.6 


160.8 


201.0 


; ^1 2 


281.4 


321.6 


361.8 


401 


j 40.1 


80.2 


120.3 


160.4 


1 200.5 


1 240.6 


280.7 


320.8 


360.9 


400 


' 40.0 


800 


120.0 


160.0 


1 2(X).0 


240.0 


280.0 


320.0 


360.0 


399 


) 39.9 


79.8 


119.7 


159.6 


1 199.5 


239.4 


279.3 


319.2 


359.1 


398 


39.8 


79.6 


119.4 


159.2 


199.0 


2:38.8 


278.6 


318.4 


358.2 


397 


39.7 


79.4 


119.1 


158.8 


: 198.5 


2:38.2 


277.9 


317.6 


357.3 


396 


39.6 


79.2 


118.8 


158.4 


: 198.0 


2:37.6 


277.2 


316.8 


356.4 


395 


39.5 


79.0 


118.5 


158.0 


i 197.5 


237.0 


276.5 


316 


355.5 



LOGAKITHMS OF NUMBERS. 



435 



No. 110 L. 041.] 














[No 


. 119 L. 078. 


N. 





1 


2 


8 


4 


5 


6 


7 


8 


9 


Diff. 


110 

1 
2 

I 

5 
6 

7 

8 
9 


041393 
5323 

9218 


1787 
5714 
9606 


2182 
6105 
9993 


2576 
6495 


2969 

6885 


3362 

7275 


3755 
7664 


4148 
8053 


4540 

8442 


4932 

8830 


393 
390 


0380 
4230 
8046 


0766 
4613 
8426 


1153 

4996 
8805 


1538 
5378 
9185 


1924 
5760 
9563 


2309 
6142 
9942 


2694 
6524 


386 
383 


053078 
6905 


3463 

7286 


3846 
7666 


0320 
4083 
7815 


379 
376 
373 


060698 
4458 
8186 


1075 

4832 
8557 


1452 

5206 

8928 


1829 
5580 
9298 


2206 
5953 
9668 


2582 
6326 


2958 
6699 


3333 
7071 


3709 
7443 


0038 
3718 
7368 


0407 
4085 
7731 


0776 
4451 
8094 


1145 

4816 
8457 


1514 

5182 
8819 


370 

366 
363 


071882 
5547 


2250 
5912 


2617 
6276 


2985 
6640 


3352 
7001 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


395 


39.5 


79.0 


118.5 


158.0 


197.5 


237.0 


276.5 


316.0 


355.5 


394 


39.4 


78.8 


118.2 


157.6 


197.0 


236.4 


275.8 


315.2 


354.6 


393 


39.3 


78.6 


117.9 


157.2 


196.5 


235.8 


275.1 


314.4 


353.7 


392 


39.2 


78.4 


117.6 


156.8 


196.0 


235.2 


274.4 


313.6 


352.8 


391 


39.1 


78.2 


117.3 


156.4 


195.5 


234.6 


273.7 


312.8 


351.9 


390 


39.0 


78.0 


117.0 


156.0 


195.0 


234.0 


273.0 


312.0 


351.0 


389 


33.9 


77.8 


116.7 


155.6 


194.5 


233.4 


272.3 


311.2 


350.1 


388 


38.8 


77.6 


116.4 


155.2 


194.0 


232.8 


271.6 


310.4 


349.2 


387 


38.7 


77.4 


116.1 


154.8 


193.5 


232.2 


270.9 


309.6 


348.3 


386 


38.6 


77.2 


115.8 


154.4 


193.0 


231.6 


270.2 


308.8 


347.4 


385 


38.5 


77.0 


115.5 


154.0 


192.5 


231.0 


269.5 


308.0 


^46. 5 


384 


38.4 


76.8 


115.2 


153.6 


192.0 


230.4 


268.8 


307.2 


345.6 


383 


38.3 


76.6 


114.9 


153.2 


191.5 


229.8 


268.1 


306.4 


344.7 


382 


38.2 


76.4 


114.6 


152.8 


191.0 


229.2 


267.4 


305.6 


343.8 


381 


38.1 


76.2 


114.3 


152.4 


190.5 


228.6 


266.7 


304.8 


342.9 


380 


38.0 


76.0 


114.0 


152.0 


190.0 


228.0 


266.0 


304.0 


342.0 


379 


37.9 


75.8 


113.7 


151.6 


189.5 


227.4 


265.3 


303.2 


341.1 


378 


37.8 


75.6 


113.4 


151.2 


189.0 


226.8 


264.6 


302.4 


340.2 


377 


37.7 


75.4 


113.1 


150.8 


188.5 


226.2 


263.9 


301.6 


339.3 


376 


37.6 


75.2 


112.8 


150.4 


188.0 


225.6 


263.2 


300.8 


338.4 


375 


37.5 


75.0 


112.5 


150.0 


187.5 


225.0 


262.5 


300.0 


337.5 


374 


37.4 


74.8 


112.2 


149.6 


187.0 


224.4 


261.8 


299.2 


336.6 


373 


37.3 


74.6 


111.9 


149.2 


186.5 


223.8 


261.1 


298.4 


335.7 


372 


37.2 


74.4 


111.6 


148.8 


186.0 


223.2 


260.4 


297.6 


334.8 


371 


37.1 


74.2 


111.3 


148.4 


185.5 


222.6 


259.7 


296.8 


333.9 


370 


37.0 


74.0 


111.0 


148.0 


185.0 


222.0 


259.0 


296.0 


333.0 


369 


36.9 


73.8 


110.7 


147.6 


184.5 


221.4 


258.3 


295.2 


332.1 


368 


36.8 


73.6 


110.4 


147.2 


184.0 


220.8 


257.0 


294.4 


331.2 


S67 


36.7 


73.4 


110.1 


146.8 


183.5 


220.2 


256.9 


293.6 


330.3 


366 


36.6 


73.2 


109.8 


146.4 


183.0 


219.6 


256.2 


292.8 


329.4 


S65 


36.5 


73.0 


109.5 


146.0 


182.5 


219.0 


255.7 


292.0 


328.5 


364 


36.4 


72.8 


109.2 


145.6 


182.0 


218.4 


254.8 


291.2 


327.6 


363 


36.3 


7'2.0 


108.9 


145.2 


181.5 


217.8 


254.1 


290.4 


326.7 


362 


36.2 


72.4 


108.6 


144.8 


181.0 


217.2 


253.4 


289.6 


325.8 


361 


36.1 


72.2 


108.3 


144.4 


180.5 


216.6 


252.7 


288.8 


324.9 


360 


36.0 


72.0 


108.0 


144.0 


180.0 


216.0 


252.0 


288.0 


324.0 


359 


o5 . 9 


71.8 


107.7 


113.6 


179.5 


215.4 


251.3 


287.2 


823.1 


358 


35.8 


71.6 


107.4 


143.2 


179.0 


214.8 


250.6 


286.4 


322.2 


357 


35.7 


71.4 


107.1 


142 8 


178.5 


214.2 


249.9 


285.0 


321.3 


350 


;:." . (. 


Tl . i 


]()(). 8 


142.4 


17S.0 


213.6 


219.2 


284.8 


cj:o.4 



436 



LOGARITHMS OF KUMBERS. 



Ko. 120 L. 079.] 



[No. 134 L. 130. 



N. 



130 

1 
2 
3 

4 
5 

6 

7 
8 

Q 
130 



079181 i 9543 



082785 
6360 
9905 



3144 
6716 



9904 



3503 
7071 



3861 



093422 
6910 



100371 
3804 
7210 



110590 

8943 
7271 



120574 
3852 
7105 



0258 i 0611 0963 
3772 I 4122 1 4471 
7257 I 7604 7951 



0715 1059 1403 
4146 I 4487 i 4828 
7549 I 7888 | 8227 



0926 

4277 
7603 



0903 
4178 
7429 



1263 

4611 
7934 



1231 
4504 
7753 



1599 

4944 
8265 



1560 
4830 
8076 



I 



0626 
4219 

7781 



1315 

4820 



0987 
4576 
8136 



1747 
5169 
8565 



1667 
5169 
8644 



2091 
5510 



1934 

5278 
8595 



1888 
5156 
8399 



2270 
5611 



2216 
5481 

8722 



1347 



1707 



4934 5291 
8490 8845 



2018 
5518 
8990 



2370 

5866 
9335 



2434 
5851 
9241 



2605 

5943 
9256 



2544 
5806 
9045 



2777 
6191 
9579 



2940 

6276 
9586 



2871 
6131 



8 



2067 
5647 



2721 
6215 
9681 



3119 
6531 
9916 



3275 

6608 
9915 



3198 
6456 
9690 



9 Diff. 



2426 

6004 
9552 



3071 



0026 
a462 
6871 



0253 
3609 

6940 



0245 
3525 

6781 



0012 



Proportional, Parts. 



DiiX 



355 
354 
353 
352 
351 
3.50 
349 
348 
347 
316 

315 
314 
34:3 
342 
341 
3W 
.3:39 
338 
a37 
3:36 

335 
3U 
;i33 
332 
:i}l 
330 
3>9 
328 
327 
326 

325 
:324 
323 
322 



35.5 
35.4 
35.3 
35.2 
35.1 
35.0 
34.9 
34.8 
34.7 
34.6 

34.5 
34.4 
a4.3 
34.2 
34.1 
34.0 
.33.9 
33.8 
33.7 
33.6 

33.5 
J3;3.4 
3^3.3 
.33.2 
33.1 
33.0 
32.9 
32.8 
32.7 
32.6 

32.5 
32.4 
32.3 
32.2 



71.0 
70.8 
70.6 
70.4 
70.2 



' vu.u 
09.8 


' 69.6 


69.4 


69.2 


69.0 


68.8 


68.6 


68.4 


68.2 


68.0 


67.8 


67.6 


07.4 


67.2 


67.0 


66.8 


66.6 


66.4 


66.2 


66.0 


65.8 


65.6 


65.4 


65.2 


65.0 


64.8 


64.6 


W.4 



106.5 
106.2 
105.9 
105.6 
105.3 
105.0 
104.7 
104.4 
104.1 
103.8 

103.5 

103.2 

102.9 i 

102.6 

102.3 

102.0 

101.7 

101.4 

101.1 

100.8 

100.5 
100.2 
99.9 
99.6 
99.3 
99.0 
98.7 
98.4 
98.1 
97.8 

07.5 
97.2 
96.9 
96.6 



142.0 
141.6 
141.2 
140.8 
140.4 
140.0 
139.6 
139.2 
138.8 
138.4 

138.0 
137.6 
137.2 
136.8 
136.4 
136.0 
1:35.6 
135.2 
134.8 
134.4 

134.0 
133.6 
ia3.2 
132.8 
132.4 
132.0 
131.6 
131.2 
130.8 
1:30.4 

130.0 
129.6 
129.2 
128. S 



177.5 

177.0 

176.5 

176.0 

175.5 I 

175.0 

174.5 

174.0 

173.5 

173.0 

172.5 
172.0 
171.5 
171.0 
170.5 
170.0 
109.5 
169.0 
168.5 
168.0 

167.5 
167.0 
166.5 
166.0 
165.5 
165.0 
164.5 
164.0 
1(>3.5 
163.0 

162.5 
102.0 
161.5 
161.0 



6 


7 


8 


9 


213.0 


248.5 


284.0 


319.5 


( 212.4 


^7.8 


283.2 


318.6 


211.8 


247.1 


282.4 


317.7 


1 211.2 


246.4 


281.6 


316.8 


1 210.6 


^5.7 


280.8 


315.9 


1 210.0 


245.0 


280.0 


315.0 


1 209.4 


244.3 


279.2 


314.1 


i 208.8 


243.6 


278.4 


313.2 


208.2 


242.9 


277.6 


312.3 


207.6 


^42. 2 


276.8 


311.4 


207.0 


241.5 


276.0 


310.5 


206.4 


240.8 


275.2 


309.6 


205.8 


340.1 


274.4 


308.7 


205.2 


239.4 


273.6 


307.8 


204.6 


238.7 


272.8 


306.9 


204.0 


238.0 


272.0 


306.0 


203.4 


237.3 


271.2 


305.1 


202.8 


236.6 


270.4 


304.2 


202.2 


235.9 


269.6 


303.3 


201.6 


235.2 


268.8 


302.4 


201.0 


234.5 


268.0 


301.5 


200.4 


233.8 


267.2 


300.6 


199.8 


233.1 


266.4 


299.7 


199.2 


232.4 


265.6 


298.8 


198.6 


231.7 


264.8 


297.9 


198.0 


231.0 


264.0 


297.0 


197.4 


230.3 


263.2 


296.1 


196.8 


229.6 


262.4 


295.2 


196.2 


228.9 


261.6 


294.3 


195.6 


228.2 


260.8 


293.4 


195.0 


227.5 


260.0 


292.5 


194.4 


226.8 


259.2 


291.6 


193.8 


226.1 


258.4 290.7 


193.2 


22r» J 




289.8 



LOGARITHMS OF NUMBERS. 



437 



No. 


135 L. 130.] 














[No. 149 L. 175. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


135 
6 

r 

8 


i30334 
3539 
6721 
9879 


0655 

3858 
7037 


0977 
4177 
7354 


1298 
4496 
7671 


1619 

4814 
7987 


1939 
5133 
8303 


2260 
5451 

8618 


2580 
5769 
8934 


2900 
6086 
9249 


3219 
6403 
9564 


321 
318 
316 


0194 
3327 

6438 
9527 


0508 
3639 

6748 
9835 


0822 
3951 

7058 


1136 

4263 

7367 


1450 
4574 

7676 


1763 

4885 

7985 


2076 
5196 

8294 


2389 
5507 

8603 


2702 
5818 

8911 


314 


9 

140 
1 


143015 

6128 
9219 


311 
309 


0142 
3205 
6246 
9266 


0449 
3510 
6549 
9567 


0756 
3815 
6852 
9868 


1063 
4120 
7154 


1370 
4424 

7457 


1676 
4728 
7759 


1982 
5032 
8061 


307 


2 
3 

4 


152288 
5336 
8362 


2594 
5640 
8664 


2900 
5943 
8965 


305 
303 


0168 
3161 
6134 

9086 


0469 
3460 
6430 
9380 


0769 
3758 
6726 
9674 


1068 
4055 
7022 
9968 


301 


5 
6 

7 


161368 
4353 

7317 


1667 
4650 
7613 


1967 
4947 
7908 


2266 
5244 
8203 


2564 
5541 
8497 


2863 
5838 
8792 


299 
297 
295 


8 
9 


170262 
3186 


0555 
3478 


0848 
3769 


1141 
4060 


1434 
4351 


1726 
4641 


2019 
4932 


2311 
5222 


2603 
5512 


2895 
5802 


293 

291 



Proportional Parts. 



821 

320 
319 
318 
317 
316 
315 
314 
313 
312 

311 
310 

309 
308 
307 
306 
305 
304 
303 
302 

301 
300 
299 
298 
297 
296 
295 
294 
293 
292 

291 

290 

289 
288 
2S7 
286 



1 


2 


32.1 


64 2 


32.0 


64.0 


31.9 


63.8 


31.8 


63.6 


31.7 


63.4 


31.6 


63.2 


31.5 


63.0 


31.4 


62.8 


31.3 


62.6 


31.2 


62.4 


31 1 


62.2 


31.0 


62.0 


30.9 


61.8 


30.8 


61.6 


30.7 


61.4 


30.6 


61.2 


30.5 


61.0 


30.4 


60.8 


30.3 


60.6 


30.2 


60.4 


30.1 


60.2 


30.0 


60.0 


29.9 


59.8 


29.8 


59.6 


29.7 


59.4 


29.6 


59.2 


29.5 


59.0 


29.4 


58.8 


29.3 


58.6 


29.2 


58.4 


29.1 


58.2 


29.0 


58.0 


28.9 


57.8 


28.8 


57.6 


28.7 


57.4 


28.6 


57.2 



3 


4 


5 


6 


7 


8 


9 


96.3 


128.4 


160.5 


192.6 


224.7 


256.8 


288.9 


96.0 


128.0 


160.0 


192.0 


224.0 


256.0 


288.0 


95.7 


127.6 


159.5 


191.4 


223.3 


255.2 


287.1 


95.4 


127.2 


159.0 


190.8 


222.6 


254.4 


286.2 


95.1 


126.8 


158.5 


190.2 


221.9 


253.6 


285.3 


94.8 


126.4 


158.0 


189.6 


221.2 


252.8 


284.4 


94.5 


126.0 


157.5 


189.0 


220.5 


252.0 


283.5 


94.2 


125.6 


157.0 


188.4 


219.8 


251.2 


282.6 


93.9 


125.2 


156.5 


187.8 


219.1 


250.4 


281.7 


93.6 


124.8 


156.0 


187.2 


218.4 


249.6 


280.8 


93.3 


124.4 


155.5 


186.6 


217.7 


248.8 


279.9 


93.0 


124.0 


155.0 


186,0 


217.0 


248.0 


279.0 


92.7 


123.6 


154.5 


185.4 


216.3 


247.2 


278.1 


92.4 


123.2 


154.0 


184.8 


215.6 


246.4 


277.2 


92.1 


122.8 


153.5 


184.2 


214.9 


245 6 


276.3 


91.8 


122.4 


153.0 


183.6 


214.2 


244,8 


275.4 


91.5 


122.0 


152.5 


183.0 


213.5 


244.0 


274,5 


91.2 


121.6 


152.0 


182.4 


212.8 


243 2 


273.6 


90.9 


121.2 


151.5 


181.8 


212.1 


242.4 


272.7 


90.6 


120.8 


151.0 


181.2 


211.4 


241.6 


271.8 


90.3 


120.4 


150.5 


180.6 


210.7 


240,8 


270.9 


90.0 


120.0 


150.0 


180.0 


210.0 


240.0 


270.0 


89.7 


119.6 


149.5 


179.4 


209.3 


239.2 


269.1 


89.4 


119.2 


149.0 


178.8 


208.6 


238.4 


268.2 


89.1 


118.8 


148.5 


178.2 


207.9 


237.6 


267.3 


88.8 


118.4 


148.0 


177.6 


207.2 


236.8 


266.4 


88.5 


118.0 


147.5 


177.0 


206.5 


236.0 


265.5 


88.2 


117.6 


147.0 


176.4 


205.8 


235.2 


264.6 


87.9 


117.2 


146.5 


175.8 


205.1 


234.4 


263.7 


87.6 


116.8 


146.0 


175.2 


204.4 


233.6 


262.8 


87.3 


116.4 


145.5 


174.6 


203.7 


232.8 


261.9 


87.0 


116.0 


145.0 


174.0 


203.0 


232.0 


261.0 


86.7 


115.6 


144.5 


173.4 


202.3 


231.2 


260.1 


86.4 


115.2 


144.0 


172.8 


201.6 


2;U).4 


250.2 


86.1 


114.8 


113.5 


172.2 


200.9 


229.6 


258.3 


85.8 


114.4 


ti'VO 


171.6 


200.2 


228.8 


257.4 



438 



LOGARITHMS OF NUMBERS 



No. 150 L. 176.] 



[No. 169 L. 230. 



N. 





1 


2 


3 


4 


5 ' 


6 


7 


8 


9 


Diff. 


150 
1 

2 
3 

4 


176091 
8977 

181^44 
4691 
7521 


6381 
92^4 

2129 
4975 
7803 


6u70 
9552 

^15 
5259 

8084 


6959 
9839 

2700 
5542 
8366 


7248 

0126 

2985 
5825 
8647 


7536 


7825 


8113 


8401 


8689 


289 


0413 
3270 
6108 

8928 


0699 
3555 
6:^91 
9209 


0986 
3839 
6674 
^90 


1272 
4123 
6956 
9771 


1558 
4407 
7239 

0051 
2846 
5623 

8382 


287 
285 
283 

281 
279 

278 
276 


5 
6 
7 

8 


190332 
3125 
5900 
8657 


0612 
a403 
6176 
8932 


0892 
3681 
6453 
9206 


1171 
3959 
6729 
9481 


1451 
4237 
7005 
9755 


1730 
4514 
7281 


2010 
4792 
7556 


2289 
5069 
7832 


2567 
5346 
8107 


0029 
2761 

5475 
8173 


0303 
3033 

5746 
8441 


0577 
3305 

6016 
8710 


0850 
3577 

6286 
8979 


1124 

3848 

6556 
9-247 


274 
272 

271 
269 


9 

160 

1 
2 


201397 

4120 
6826 
9515 


1670 

4391 
7096 
9783 


1943 

4663 
7365 

0051 
2720 
5373 
8010 


2216 

49^4 
76:34 

0319 
2986 
56:38 
8273 


5204 
7904 

0586 
3252 
5902 
8536 


0853 
3518 
6166 
8798 


1121 
3783 
6430 
9060 


1388 
4049 
6694 
9323 


1654 
4314 
6957 
9585 


1921 
4579 
7221 
9846 


267 
266 
264 
262 


3 

4 
5 


212188 
4844 
7484 


^454 
5109 
7747 


6 

8 
9 


220108 
2716 
5309 

7887 
23 


0370 
2976 
5.568 
8144 


0631 
3-236 

5826 

8400 


0892 
a496 
6084 

8657 


115:3 
3755 
6:312 
8913 


1414 
4015 
66CK) 
9170 


1675 
4274 

6858 
9426 


1936 
4533 
7115 
9682 


2196 
4792 
7372 
9938 


2456 
5051 
7630 

0193 


261 
259 
258 

256 



Proportional Parts. 



Diff. 


1 


o 


3 


4 


5 


6 


7 


8 


9 


•285 


28.5 


57.0 


85.5 


114.0 


142.5 


171.0 


199.5 


228.0 


256.5 


284 


28.4 


56.8 


85.2 


113.6 


142.0 


170.4 


198.8 


227.2 


255.6 


283 


28-3 


56.6 


84.9 


113.2 


141.5 


169.8 


198.1 


226.4 


254.7 


282 


28.2 


56.4 


84.6 


112.8 


141.0 


169.2 


197.4 


225.6 


253.8 


281 


28.1 


56.2 


84.3 


112 4 


140.5 


168.6 


196.7 


224-8 


252.9 


280 


28.0 


56.0 


84.0 


112.0 


140.0 


168.0 


196.0 


224.0 


252.0 


279 


27.9 


55.8 


83.7 


111.6 


139.5 


167.4 


195.3 


223.2 


251.1 


278 


27.8 


55.6 


83.4 


111.2 


139.0 


166.8 


194.6 


222.4 


250.2 


277 


27.7 


55.4 


83.1 


110.8 


138.5 


166.2 


193.9 


221.6 


249.3 


276 


27.6 


55.2 


82.8 


110.4 


138.0 


165.6 


193.2 1 


220.8 


248.4 


275 


27.5 


55.0 


82.5 


110.0 


137.5 


165.0 


192.5 i 


220.0 


217.5 


274 


27.4 


54.8 


82.2 


109.6 


137.0 


164.4 


191.8 


219.2 


246.6 


273 


27.3 


54.6 


81.9 


109.2 


136.5 


163.8 


191.1 


pSA 


245.7 


272 


27.2 


54.4 


81.6 


106.8 


136.0 


163.2 


190.4 


S17.6 


244.8 


.271 


27.1 


54.2 


81.3 


108.4 


135.5 


162.6 


189.7 


216.8 


243.9 


270 


27.0 


54-0 


81.0 


108.0 


135.0 


162.0 


189.0 


216.0 


243.0 


269 


26.9 


53.8 


80.7 


107.6 


1^4-5 


161.4 


188.3 ! 


215.2 


242.1 


268 


26.8 


53.6 


80.4 


107.2 


m.o 


160.8 


187.6 


214.4 


241.2 


267 


26.7 


53.4 


80.1 


106.8 


133.5 


160.2 


186.9 1 


213.6 


240.3 


266 


26.6 


53.2 


79.8 


106.4 


133.0 


159.6 


186.2 


212.8 


239.4 


265 


26.5 


53.0 


79.5 


106.0 


132.5 


159.0 


185.5 


212.0 


238.5 


264 


26.4 


52.8 


79.2 


105.6 


132.0 


158.4 


184.8 ' 


211.2 


237.6 


26:3 


26.3 


52.6 


78.9 


105.2 


131.5 


157.8 


184.1 


210.4 


236.7 


262 


26.2 


52.4 


78.6 


104.8 


131.0 


157.2 


183.4 


209.6 


235.8 


261 


26.1 


52-2 


78.3 


104.4 


130.5 


156.6 


182.7 


208.8 


2^4.9 


260 


26.0 


52.0 


78.0 


104.0 


130.0 


156.0 


182.0 


208-0 


234.0 


259 


25.9 


51.8 


77.7 


103.6 


129.5 


155.4 


181.3 


207.2 


233.1 


?58 


25.8 


51.6 


77.4 


103 2 


120.0 


154 8 


180.6 


206.4 


Ctpo «> 


257 


25.7 


51.4 


77.1 


102.8 


128.5 


154.2 


179.9 


205.6 


iJ.c 


256 


25.6 


51.2 


76.8 


102.4 


128.0 


153.6 


179.2 


204.8 


230.4 


255 


25.5 


51.0 


76.5 


K«.0 


1^7.5 


153.0 


178.5 : 


204.0 


229.5 



LOGAKITHMS OP NITMBEKS. 



439 



No. 


170 L. 230.] 














[N 


o. 109 L. 278. 


N. 





I 


2 


8 


4 


5 


6 


7 


8 


9 


Dm. 


170 
1 
2 
3 


230449 
2996 

5528 
8046 


0704 
3250 
5781 
8297 


0960 
3504 
6033 

8548 


1215 
3757 

6285 
8799 


1470 
4011 
6537 
9049 


1724 
4264 
6789 
9299 


1979 
4517 
7041 
9550 


2234 
4770 
7292 
9800 


2488 
5023 
7544 


2742 
527G 
7795 


255 
253 
252 


0050 
2541 
5019 

7482 
9932 


0300 
27'90 
5266 

7728 


250 
24J 

248 
^G 


4 
5 

G 

7 


240549 
3038 
5513 
7973 


0799 
3286 
5759 
8219 


1048 
3534 
6006 
8464 


1297 

3782 
6252 
8709 


1546 
4030 
6499 
8954 


1795 
4277 
6745 
9198 


2044 
4525 
6991 
9443 


2293 
4772 
7257 
9687 


0176 
2610 
5031 

7'439 

9833 


245 

243 
^2 

241 
239 


8 
9 

180 

1 


250420 
2853 

5273 
7679 


0664 
3096 

5514 
7918 


0908 
3338 

5755 

8158 


1151 
3580 

5996 
8398 


1395 

3822 

6237 

8637 


1G38 
4064 

6477 

8877 


IGOl 
4306 

6718 
9116 


21C5 
4548 

6958 
9355 


2868 
4790 

7198 
9594 


2 
3 
4 
5 
6 


260071 
2451 
4818 
7172 
9513 


0310 
2688 
5054 
7406 
9746 


0548 
2925 
5290 
7641 
9980 


0787 
3162 
5525 

7875 


1025 
3399 
5761 
8110 


1203 
3636 
5996 
8344 


inci 

3873 
6232 

8578 


1739 

4109 
6467 

8812 


1976 
4346 
6702 
9046 


2214 

4582 
C937 
9279 


238 
237 
235 
234 


0213 
2538 
4850 
7151 


0446 

2770 
5081 
7380 


0679 
3001 
5311 
7609 


0912 
3233 

5542 

7838 


1144 
3464 

5772 
8067 


1377 
3696 
6002 
8296 


1609 
3927 
6232 

8525 


233 
232 
230 

229 


7 
8 
9 


271842 
4158 
6462 


2074 
4389 
6692 


2306 
4620 
6921 



Proportional Parts. 



Diff. 


1 


2 


3 


'4 


5 


6 


7 


8 


9 


255 


25.5 


51.0 


76.5 


102.0 


127.5 


153.0 


178.5 


204.0 


229.5 


254 


25.4 


50.8 


76.2 


101.6 


127.0 


152.4 


177.8 


203.2 


228.6 


253 


25.3 


50.6 


75.9 


101.2 


126.5 


151.8 


177.1 


202.4 


227.7 


252 


25.2 


50.4 


75.6 


100.8 


126.0 


151.2 


176.4 


201.6 


226.8 


251 


25.1 


50.2 


75.3 


100.4 


125.5 


150.6 


175.7 


200.8 


225.9 


250 


25 


50.0 


75.0 


100.0 


125.0 


1.50.0 


175.0 


200.0 


225.0 


249 


24.9 


49.8 


74.7 


99.6 


124.5 


149.4 


174.3 


199.2 


224.1 


248 


24.8 


49.6 


74.4 


99.2 


124.0 


148.8 


17'3.6 


198.4 


223.2 


247 


24.7 


49.4 


74.1 


98.8 


123.5 


148.2 


172.9 


197.6 


222.3 


246 


24.6 


49.2 


73.8 


98.4 


123.0 


147.6 


172.2 


196.8 


221.4 


245 


24.5 


49.0 


73.5 


98.0 


122.5 


147.0 


171.5 


196.0 


220.5 


244 


24.4 


48.8 


73.2 


97.6 


122.0 


146.4 


170.8 


195.2 


219.6 


243 


24.3 


48.6 


72.9 


97.2 


121.5 


145.8 


170.1 


194.4 


218.7 


242 


24.2 


48.4 


72.6 


96.8 


121.0 


145.2 


169.4 


193.6 


217.8 


241 


24.1 


48.2 


72.3 


96.4 


120.5 


144.6 


168.7 


192.8 


216.9 


240 


24.0 


48.0 


72.0 


96.0 


120.0 


144.0 


168.0 


192.0 


216.0 


239 


23.9 


47.8 


71.7 


95.6 


119.5 


143.4 


167.3 


191.2 


215.1 


238 


23.8 


47.6 


71.4 


95.2 


119.0 


142.8 


166.6 


190.4 


214.2 


237 


23.7 


47.4 


71.1 


94.8 


118.5 


142.2 


165.9 


189.6 


213.3 


236 


23.6 


47.2 


70.8 


94.4 


118.0 


141.6 


165.2 


188.8 


212.4 


235 


23.5 


47.0 


70.5 


94.0 


117.5 


141.0 


164.5 


188.0 


211.5 


234 


23.4 


46.8 


70.2 


93.6 


117.0 


140.4 


163.8 


187.2 


210.6 


233 


23.3 


46.6 


69.9 


93.2 


116.5 


139.8 


163.1 


186.4 


209.7 


232 


23.2 


46.4 


69.6 


92.8 


116.0 


139.2 


162.4 


185.6 


208.8 


231 


23.1 


46.2 


69.3 


92.4 


115.5 


138.6 


161.7 


184.8 


207.9 


230 


23.0 


46.0 


69.0 


92.0 


115.0 


138.0 


161.0 


184.0 


207.0 


229 


22.9 


45.8 


68.7 


91.6 


114.5 


137.4 


160.3 


183.2 


206.1 


228 


22.8 


45.6 


68.4 


91.2 


114.0 


136.8 


159.6 


182.4 


205.2 


227 


22.7 


45.4 


68.1 


90.8 


113.5 


136.2 


158.9 


181.6 


201.3 


226 


22.6 


45.2 


67.8 


90.4 


113.0 


135.6 


158 2 


1H0.8 


203.4 



440 



LOGARITHMS OF KtTMBERS. 



No. 190 L. 278.] 



[No. 214 L. Z%.. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




278754 


8982 


9211 


9439 


9667 


9895 












190 


0123 
2396 
4656 
6905 
9143 


0351 

2622 
4882 
7130 
9366 


0578 
2849 
5107 
7354 
9589 


0806 
3075 
5332 

7578 
9812 


228 
227 
226 
225 
223 


1 

2 
3 

4 


281033 
3301 
5557 

7802 


1261 
3527 

5782 
8026 


1488 
3753 
6007 
8249 


1715 
3979 
6232 
8473 


1942 
4205 
6456 
8696 


2169 
4431 
6681 
8920 


5 
6 

7 
8 
9 


290035 
2256 
4466 
6665 
8853 


0257 

^78 
4687 
6884 
9071 


0480 
2699 
4907 
7104 
9289 


0702 
2920 
5127 
7323 
9507 


0925 
3141 
5347 
7542 
9725 


1147 
3363 
5567 
7761 
9943 


1369 
3584 

5787 
7979 


1591 
3804 
6007 
8198 


1813 
4025 
6226 
8416 


2034 
4246 
6446 
8635 


223 
221 
220 
219 




0101 

2331 
4491 
6639 

8778 


0378 

2547 
4706 
6854 
8991 


0595 

2764 
4921 
7068 
9204 


0813 

2980 
5136 
7282 
9417 


218 

217 
216 
215 
213 


200 
1 
2 
3 
4 


301030 
3196 
5351 
7496 
9630 


1247 
3412 
5566 
7710 
9843 


1464 

3628 
5781 
7924 


1681 
3844 
5996 
8137 


1898 
4059 
6211 
8351 


2114 
4275 
6425 
8564 




0056 
2177 
4289 
6390 
8481 


0268 
2389 
4499 
6599 
8689 


0481 
2600 
4710 
6809 
8898 


0693 

2812 

4920 

! 7018 

' 9106 


0906 
3023 
6130 
7227 
9314 


1118 
3234 
5340 
7436 
9522 


1330 
3445 
5551 
7646 
9730 


1542 
3656 
5760 
7854 
9938 


212 
211 
210 
209 
208 


5 
6 

7 
8 


311754 

3867 
5970 
8063 


1966 
4078 
6180 
8272 


9 

210 
1 
2 
3 


320146 

2219 

4282 
6336 
8380 


0354 

2426 

4488 
6541 
8583 


0562 

2633 

4694 
67'45 

8787 


0769 

2839 

4899 
6950 
8991 


0977 

3046 
5105 
7155 
9194 


1184 

3252 

5310 

7359 

1 9398 


1391 

3458 
5516 
7563 
9601 


1598 

3665 
5721 

7767 
9805 


1805 

3871 
5926 
7972 


2012 

4077 
6131 
8176 


207 

206 
205 
204 




0008 
2034 


0211 
2236 


203 
202 


4 


330414 


0617 


0819 


1022 


1225 


1 1427 


1630 


1832 



PROPORTioNAii Parts. 



Diff. 



225 
224 
223 
222 
221 
220 
219 
218 

217 
216 
215 
214 
213 
212 
211 
210 

209 
208 
207 
206 
205 
204 
203 
202 



22.5 


45.0 


22.4 


44.8 


22.3 


44.6 


22.2 


44.4 


22.1 


44.2 


22.0 


44.0 


21.9 


43.8 


21.8 


43.6 


21.7 


43.4 


21.6 


43.2 


21.5 


43.0 


21.4 


42.8 


21.3 


42.6 


21.2 


42.4 


21.1 


42.2 


21.0 


42.0 


20.9 


41.8 


20.8 


41.6 


20.7 


41.4 


20.6 


41.2 


20.5 


41.0 


20.4 


40.8 


20.3 


40.6 


20.2 


40.4 



67.5 
67.2 
66.9 
66.6 
66.3 
66.0 
65.7 
€5,4 

65.1 
64.8 
64.5 
64.2 
63.9 
63.6 
63.3 
63.0 

62.7 
62.4 
62.1 
61.8 
61.5 
61.2 
60.9 
60.6 



90.0 
89.6 
89.2 
88.8 
88.4 
88.0 
87.6 
87.2 

86.8 
86.4 
86.0 
85.6 
85.2 
84.8 
84.4 
84.0 

83.6 
83.2 

82.8 
82.4 
82.0 
81.6 
81.2 
'X).8 



112.5 
112.0 
111.5 
111.0 
110.5 
110.0 
109.5 
109.0 

108.5 
108.0 
107.5 
107.0 
106.5 
106.0 
105.5 
105.0 

104.5 
104.0 
103.5 
103.0 
109.5 
102.0 
101.5 
101.0 



135.0 
134.4 
133.8 
133.2 
132.6 
132.0 
131.4 
130.8 

130.2 
129.6 
129.0 
128.4 
127.8 
127.2 
126.6 
126.0 

125.4 
124.8 
124.2 
123.6 
1?3.0 
122.4 
121.8 
121.2 



157.5 
156.8 
156.1 
155.4 
154.7 
154.0 
153.3 
152.6 

151.9 
151.2 
150.5 
149.8 
149.1 
148.4 
147.7 
147.0 

146.3 
145.6 
144.9 
144.2 
143.5 
142.8 
142.1 
141.4 



180.0 


202.5 


179.2 


201.6 


178.4 


200.7 


177.6 


199.8 


176.8 


198.9 


176.0 


198.0 


175.2 


197.1 


174.4 


196.2 


173.6 


195.3 


172.8 


194.4 


172.0 


193.5 


171.2 


192.6 


170.4 


191.7 


169.6 


190.8 


168.8 


189.9 


168.0 


189.0 


167.2 


188.1 


166 4 


187.2 


165.6 


186.3 


164.8 


185.4 


164.0 


1&1.5 


163.2 


1&3.0 i 


162.4 


182.7 ; 


161.6 


181.8 



LOGARITHMS OF i^UMBERS. 



441 



No. 215 L. 332.] 



[No. 239 L. 380. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


215 
6 

7 
8 


332438 
4454 
6460 
8456 


2640 
4655 
€660 
.8656 


2842 
4856 
6860 
8855 


3044 
50&7 
7060 
9054 


3246 
5257 
7260 
9253 


3447 
5458 
7459 
9451 


3649 

5658 
7659 
9650 


3850 
5859 
7858 
9849 


4051 
6059 
8058 


4253 
6260 

8257 


202 
201 
200 


0047 
2028 

3999 
5962 
7915 
9860 

1796 
3724 
5643 
7554 
9456 


0246 
2225 

4196 
6157 
8110 


199 
198 

197 
196 
195 


9 

220 
1 
2 
3 


340444 

2423 
4392 
6353 
8305 


0642 

2620 
4589 
6549 
8500 


0841 

2817 

47'85 
6744 
8694 


1039 

3014 
4981 
6939 

8889 


1237 

3212 
5178 
7135 
9083 


1435 

3409 
5374 
7330 
9278 


1632 

3606 
5570 
7525 
9472 


1830 

3802 
5766 
7720 
9666 


0054 
1989 
3916 
5834 

7744 
9646 


194 
193 
193 
192 
191 
190 


4 
5 
6 

7 
8 
9 


350248 
2183 
4108 
6026 
7935 
9835 


0442 
2375 
4301 
6217 
8125 


0636 
2568 
4493 
6408 
8316 


0829 
2761 
4685 
6599 
8506 


1023 
2954 
4876 
6790 
8696 


1216 
3147 
5068 
6981 

8886 


1410 
3339 
5260 
7172 
9076 


1603 
3532 
5452 
7363 
9266 


0025 

1917 
3800 
5675 
7542 
9401 


0215 

2105 
3988 
5862 
7729 
9587 


0404 

2294 
4176 
6049 
7915 
9772 


0593 

2482 
4363 
6236 
8101 
9958 


0783 

2671 
4551 
6423 

8287 


0972 

2859 
4739 
6610 
8473 


1161 

3048 
4926 
6796 
8659 


1350 

3236 
5113 
6983 
8845 


1539 

3424 
5301 
7169 
9030 


189 

188 
188 
187 
186 


230 
1 
2 
3 

4 


361728 
3612 
5488 
7356 
9216 




0143 
1991 
3831 
5664 
7488 
9306 


0328 
2175 
4015 
5846 
7670 
9487 


0513 
2360 
4198 
6029 

7852 
9668 


0698 
2544 
4382 
6212 
8034 
9849 


0883 
2728 
4565 
6394 
8216 


185 
184 
184 
183 
182 


5 
6 

7 
8 
9 


371068 
2912 
4748 
6577 
8398 

38 


1253 
3096 
4932 
6759 
8580 


1437 
3280 
5115 
6942 

mi 


1622 
3464 
5298 
7124 
8943 


1806 
3647 
5481 
7306 
9124 


0030 


181 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


202 


20.2 


40.4 


60.6 


80.8 


101.0 


121.2 


141.4 


161.6 


iai.8 


201 


^0.1 


40.2 


60.3 


80.4 


100.5 


120.6 


140.7 


160.8 


180.9 


200 


20.0 


40.0 


60.0 


80.0 


100.0 


120.0 


140.0 


160.0 


180.0 


199 


19.9 


39.8 


59.7 


79.6 


99.5 


119.4 


139.3 


159.2 


179.1 


198 


19.8 


39.6 


59.4 


79.2 


99.0 


118.8 


138.6 


158.4 


178.2 


197 


19.7 


39.4 


59.1 


78.8 


98.5 


118.2 


137.9 


157.6 


177.3 


196 


19.6 


39.2 


58.8 


78.4 


98.0 


117.6 


137.2 


156.8 


176 4 


195 


19.5 


39.0 


58.5 


78.0 


97 5 


117.0 


136.5 


156.0 


175.5 


194 


19.4 


38.8 


58.2 


77.6 


97.0 


116.4 


135.8 


155.2 


174.6 


193 


19.3 


38.6 


57.9 


77.2 


96.5 


115.8 


135.1 


154.4 


173 7 


192 


19.2 


38.4 


57.6 


76.8 


96.0 


115.2 


134.4 


153.6 


172.8 


191 


19.1 


38.2 


57.3 


76.4 


95.5 


114.6 


133.7 


152.8 


171.9 


190 


19.0 


38.0 


57.0 


76.0 


95.0 


114.0 


133.0 


152.0 


171.0 


189 


18.9 


37.8 


56.7 


75.6 


94.5 


113.4 


132.3 


151.2 


170.1 


188 


18.8 


37.6 


56.4 


75.2 


94.0 


112.8 


131.6 


150.4 


169.2 


187 


18.7 


37 4 


56.1 


74.8 


93.5 


112.2 


130.9 


149.6 


168.3 


186 


18.6 


37.2 


55.8 


74.4 


93.0 


111.6 


130.2 


148.8 


167.4 


185 


18.5 


37.0 


55.5 


74.0 


92.5 


111.0 


129.5 


148.0 


166.5 


184 


18.4 


36.8 


55.2 


73.6 


92.0 


110.4 


128.8 


147.2 


165.6 


183 


18.3 


36.6 


54.9 


73.2 


91.5 


109.8 


128.1 


146.4 


164.7 


182 


18.2 


36.4 


54.6 


72.8 


91.0 


109.2 


127.4 


145.6 


163.8 


181 


18.1 


36.2 


54.3 


72.4 


90.5 


108.6 


126.7 


144.8 


162.9 


180 


18.0 


36.0 


54.0 


72.0 


90.0 


108.0 


126.0 


144.0 


162.0 


179 


17.9 


35.8 


53.7 


71.6 


89.5 


107.4 


125.3 


143.2 


161.1 



442 



LOGARITHMS OF LUMBERS. 



No. 


MO L. 380.] 














[N 


0. 269 L. 431 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Dm. 


U) 


380211 


0392 


0573 


0754 


0934 


1115 


1296 


1476 


1656 


1837 


xSi 


1 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3630 


180 


'^ 


3815 


3995 


4174 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


8 


5606 


5785 


5964 


61 42 


6321 


6499 


6677 


6856 


7034 


7212 


178 


4 


7390 


7568 


7746 


7924 


8101 


8279 


8456 


8634 


8811 


8989 


178 


5 


9166 


9343 


9520 


9698 


9875 














0051 

1817 


0228 


0405 


0582 


0750 


177 





390935 


1112 


1288 


1464 


1641 


1093 


2369 


2345 


25.21 


17(> 


T 


2697 


2873 


3048 


3224 


3400 


3575 


3751 


3926 


4101 


4277 


176 


8 


4452 


4627 


4802 


4977 


5152 


5326 


5501 


5676 


5850 


6025 


175 


9 


6199 


6374 


6548 


6722 


6896 


7071 


7245 


7419 


7592 


7765 


174 


250 


7940 


8114 


8287 


8461 


8634 


8808 


8981 


9154 


9328 


9501 


173 


1 


9674 


9847 


















0020 
1745 


0102 
1917 


0365 

2089 


1 0538 
' 22C1 


0711 

2433 


0888 
2605 


1056 
2777 


1228 
2949 


173 


2 


401401 


1573 


172 


3 


3121 


3292 


3464 


3635 


.3807 


3978 


4149 


4320 


4492 


4663 


171 


4 


4834 


5005 


5176 


5346 


5517 


i 5688 


5858 


6029 


6199 


6370 


171 


5 


6540 


6710 


6881 


7051 


7221 


7.-:9i 


7561 


7731 


7901 


8070 


170 


6 


8240 


8410 


8579 


8749 


8918 


1 9087 


9257 


9426 


9595 


9764 


169 




9933 
























0102 


0271 


0440 


0609 


1 0777 


0946 


1114 


1283 


1451 


169 


8 


411620 


1788 


1956 


2124 


2293 


2461 


2629 


2796 


2964 


3132 


168 


9 


3300 


3467 


3635 


3803 


3970 


4137 


4305 


4472 


4639 


4806 


167 


2m 


4973 


5140 


5307 


5474 


5641 


5808 


5974 


6141 


6308 


6474 


167 


1 


6641 


6807 


6973 


7139 


7306 


7472 


7638 


7804 


7970 


8135 


166 


2 


8301 


8467 


8633 


8793 


89G4 


9129 


9295 


9460 


9625 


9791 


165 


3 


9956 






















0121 


0286 


0451 


0G16 


0781 


0945 


1110 


1275 


1439 


165 


4 


421604 


1768 


1933 


2097 


2261 


2426 


2590 


2754 


2918 


3082 


164 


5 


3246 


3410 


3574 


3r37 


3901 


4065 


4228 


4392 


4555 


4718 


164 


6 


4882 


5045 


5208 


5371 


5534 


5697 


5860 


6023 


6186 


6349 


163 


7 


6511 


6674 


6836 


6999 


7161 


7324 


7486 


7648 


7811 


7973 


162 


8 


8135 


8297 


8459 


8621 


8783 


8944 


9106 


9268 


9429 


9591 


162 


9 


9752 
43 


9914 




















0075 


0236 


0398 


0559 


0720 


0881 1 1042 


1203 


161 



Proportional. Parts. 



mn. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


178 


17.8 


35.6 


53.4 


71.2 


89.0 


106.8 


124.6 


142.4 


160.2 


177 


17.7 


35.4 


53.1 


70.8 


88.5 


106.2 


123.9 


141.6 


159.3 


176 


17.6 


35.2 


52.8 


70.4 


88.0 


105.6 


123.2 


140.8 


158.4 


17'5 


17.5 


35.0 


52.5 


70.0 


87.5 


105.0 


122.5 


140.0 


157.5 


17'4 


17.4 


34.8 


52.2 


69.6 


87.0 


104.4 


121.8 


139.2 


156.6 


173 


17.3 


34.6 


51.9 


69.2 


86.5 


103.8 


121.1 


138.4 


155.7 


172 


17.2 


34.4 


51.6 


68.8 


86.0 


103.2 


120.4 


137.6 


154.8 


171 


17.1 


34.2 


51.3 


68.4 


85.5 


102.6 


119.7 


136.8 


153.9 


170 


17.0 


34.0 


51.0 


68.0 


85.0 


102.0 


119.0 


136.0 


153.0 


169 


16.9 


33.8 


50.7 


67.6 


84.5 


101.4 


118.3 


135 2 


152.1 


168 


16.8 


a3.6 


50.4 


67.2 


84.0 


100.8 


117.6 


134.4 


151.2 


167 


16.7 


33.4 


50.1 


66.8 


83.5 


100.2 


116.9 


133.6 


150.3 


166 


16.6 


33.2 


49.8 


66.4 


83.0 


99.6 


116.2 


132.8 


140.4 


165 


16.5 


33.0 


49.5 


66.0 


82.5 


99.0 


115.5 


132.0 


148.5 


164 


16.4 


32.8 


49.2 


65.6 


82.0 


98.4 


114.8 


131.2 


147.6 


163 


16.3 


32.6 


48.9 


65.2 


81.5 


97.8 


114.1 


130.4 


140.7 


162 


16.2 


32.4 


48.5 


64.8 


81.0 


97:2 


113.4 


129.6 


145.8 


161 


16.1 


32.2 


48.3 


64.4 


80.5 


96.6 


112.7 


128.8 


111.9 



LOGARITHMS OF LUMBERS. 



443 



No. 


270 L 431.] 














[No. 299 L. 47G. 


N. 





1 


2 


3 


4 


6 


6 


7 


8 


9 


Diff. 


J?70 
1 
2 
3 
4 
5 


431364 
2969 
4569 
6163 
7751 
9333 

440909 
2480 
4045 
5604 

7158 
8706 


1525 
3130 
4729 
6322 
7909 
9491 


1685 

3290 
4888 
6481 
8067 
9648 


1846 
3450 

5048 
6640 
8226 
9806 


2007 
3610 
5207 
6799 

8384 
9964 


2167 
3770 

5367 
6957 

8542 


2328 
3930 
5526 
7116 

87'01 


8488 
4090 
5685 

7'275 
8859 


2649 
4249 
5844 
7433 
9017 


2809 
4409 
6004 
7592 
917'5 


161 
160 
159 
159 

158 


0122 
1695 
3263 

4825 
6382 

7933 

947'8 


0279 
1852 
3419 
49S1 
6537 

8088 
9633 


0437 
2009 
3576 
5137 
6692 

8242 
9787 


0594 
2166 
3732 
5293 
6848 

8397 
9941 


0752 
2323 
3889 
5449 
7003 

8552 


158 
157 
157 
156 
155 

155 


6 

7 
8 
9 

280 
1 


1066 
2637 
4201 
5760 

7313 

8861 


1224 
2793 
4857 
5915 

7468 

Ol)1K 


1381 
2950 
4513 
6071 

7623 
9170 


1538 
3106 
4669 
6226 

7778 
9324 




0095 
1633 
3165 
4692 
6214 
77'31 
9242 


154 
154 
153 
153 
152 
152 
151 


2 
3 

4 
5 
6 

7 
8 


450249 

1786 
3318 
4845 
6366 
7882 
9392 


0403 
1940 
3471 
4997 
6518 
8033 
9543 


0557 
2093 
3624 
5150 
6670 
8184 
9694 


0711 

2247 
3777 
5302 
6821 
8336 
9845 


0865 
2400 
3930 
5454 
6973 
8487 
9995 


1018 
2553 
4082 
5606 
7125 
8638 


1172 

2706 
4235 

57'58 
7276 
8789 


1326 

2859 
4387 
5910 
7428 
8940 


1479 
3012 
4540 
6062 
7579 
9091 


0146 
1649 

3146 
4639 
6126 
7'608 
9085 


0296 
1799 

3296 

4788 
6274 
7756 
9233 


0447 
1948 

3445 

4936 
6423 

7904 
9380 


0597 
2098 

3594 

5085 
6571 
8052 
9527 


0748 
2248 

3744 
5234 
6719 
8200 
9675 


151 

150 

150 
149 
149 

148 
148 


9 

€90 
1 
2 
3 
4 
5 


460898 

2398 
3893 
5383 
6868 
8347 
9822 


1048 

2548 
4042 
5532 
7016 
8495 
9969 


1198 

2697 
4191 
5680 
7164 
8643 


1348 

2847 
4340 
5829 
7312 
8790 


1499 

2997 
4490 
5977 
7460 
8938 


0116 

1585 
3049 

4508 
5962 


0263 
1732 
3195 
4653 
6107 


0410 
1878 
3341 
4799 
6252 


0557 
2025 
3487 
4944 
6397 


0704 
2171 
3633 
5090 
6542 


0851 
2318 
3779 
5235 

6687 


0998 
2464 
3925 
5381 
6832 


1145 

2610 
4071 
5526 
6976 


147 
146 
146 
146 
145 


6 

7 
8 
9 


471292 
2756 
4216 
5671 


1438 
2903 
4362 
5816 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


161 


16.1 


32.2 


48.3 


64.4 


80.5 


96.6 


112.7 


128.8 


144.9 


160 


16.0 


32.0 


48.0 


64 


80.0 


96.0 


112.0 


128.0 


144.0 


159 


15.9 


31.8 


47.7 


63.6 


79.5 


95.4 


111.3 


127.2 


143.1 


158 


15.8 


31.6 


47 4 


63.2 


79.0 


94.8 


110.6 


126.4 


142.2 


157 


1^5.7 


31.4 


47.1 


62.8 


78.5 


94.2 


109.9 


125.6 


141.3 


156 


\r,.Q 


31.2 


46 8 


62.4 


78.0 


93.6 


109.2 


124.8 


140.4 


155 


15.5 


31.0 


46.5 


62.0 


77.5 


93.0 


108.5 


124.0 


139.5 


154 


15.4 


30.8 


46.2 


61.6 


77.0 


92.4 


107.8 


123.2 


138.6 


153 


15.3 


30.6 


45.9 


61.2 


76.5 


91.8 


107.1 


122.4 


137.7 


152 


15.2 


30.4 


45.6 


60.8 


76.0 


91.2 


106.4 


121.6 


136.8 


151 


15.1 


30.2 


45.3 


60.4 


75.5 


90.6 


105.7 


120.8 


135.9 


150 


15.0 


30.0 


45.0 


60.0 


75.0 


90.0 


105.0 


120.0 


135.0 


149 


14.9 


29.8 


44.7 


59.6 


74.5 


89.4 


104.3 


119.2 


134.1 


148 


14.8 


29.6 


44.4 


59.2 


74.0 


88.8 


103.6 


118.4 


133.2 


147 


14.7 


29.4 


44.1 


58.8 


73.5 


88.2 


102.9 


117.6 


132.3 


146 


14.6 


29.2 


43.8 


58.4 


73.0 


87.6 


102.2 


116.8 


131.4 


145 


14.5 


29.0 


43 5 


58.0 


72.5 


87.0 


101.5 


116.0 


130.5 


144' 


14.4 


28.8 


43.2 


57.6 


72.0 


86.4 


100.8 


115.2 


129.6 


143 


14.3 


28.6 


42.9 


57.2 


71.5 


85.8 


100.1 


111.4 


128.7 


142 


14.2 


28.4 


42.6 


56.8 


71.0 


85.2 


99.4 


113.6 


127.8 


141 


14.1 


28.2 


42.3 


56.4 


';■;).;■' 


84.6 


98.7 


112.8 


126.9 


140 


14.0 


28.0 


42.0 


56.0 


70.0 


81.0 


98.0 


112.0 


12().0 



444 



LOGARITHMS OF LUMBERS. 



No. 300 L. 477.] 














[No 


. 339 L. 531. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


300 


477121 


7266 


7411 


7555 


7700 


7844 


7989 


8133 


8278 


8422 


145 


1 


8566 


8711 


8855 


8999 


9143 


9287 


9431 


9575 


9719 ! 9863 | 


144 


2 


480007 


0151 


0294 


0438 


0582 


0725 


9869 


1012 ' 1156 ', 1299 1 


144 


3 


1443 


1586 


1729 


1872 


2016 ; 


2159 


2302 2445 2588 


2731 


143 


4 


2874 


3016 


3159 


3302 


3445 i 


3587 


3730 3872 4015 


4157 


143 


5 


4300 


4442 


4585 


4727 


4869 


5011 


5153 5295 5437 


5579 


142 


() 


5721 


5863 


6005 


6147 


6289 


6430 


6572 j 6714 1 6855 


6997 


142 


7 


7138 


7280 


7421 


7563 


7704 I 


7845 


7986 1 8127 ' 8269 


8410 


141 


8 


8551 


8692 


8833 


8974 


9114 


9255 


9396 ' 9537 ■ 9677 


9818 


141 


9 


9958 


















0099 


0239 


0380 


0520 


0661 


0801 




140 








j.^,^^ 


310 


491362 


1502 


1642 


1782 


1922 


2062 


2201 


2341 ! 2481 


2621 


140 


1 


2760 


2900 


3040 


3179 


a319 


3458 


3597 3737 i 3876 


4015 


139 


2 


4155 


4294 


4433 


4572 


4711 I 


4850 


4989 i 5128 1 5267 


5406 


139 


3 


5544 


5683 


5822 


5960 


6099 


6238 


6376 6515 ! 6653 


6791 


139 


4 


6930 


7068 


7206 


7344 


7483 


! 7621 


7759 7897 i 8035 


8173 


138 


5 


8311 


8448 


8586 


8724 


8862 


' 8999 


9137 9275 i 9412 


9550 


138 


(> 


9687 


9824 


9962 






















0099 
1470 


0236 
1607 


{ 0374 

1 1744 


AK-Ji nC/iQ 1 rir-QK 


0922 
2291 


137 
137 


7 


501059 


1196 


1333 


1880 


2017 ' 2154 


8 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 ; 3518 


8655 


1S6 


9 


3791 


3927 


4063 


4199 


4335 


' 4471 


4607 


4743 4878 


5014 


136 


320 


5150 


5286 


5421 


5557 


5693 


' 5828 


5964 


6099 6234 


6370 


136 


1 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 7586 


7721 


135 


2 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 8934 


9068 


135 


3 


9203 


9337 


9471 


9606 


9740 


9874 










0009 
1349 


0143 

1482 


0277 
1616 


0411 
1750 


134 
134 


4 


510545 


0679 


0813 


0947 


1081 


i 1215 


5 


1883 


2017 


2151 


2.284 


2418 


! 2551 


2684 


2818 


2951 


3084 


133 


6 


3218 


3351 


3484 


3617 


3750 


3883 


4016 


4149 


4282 


4415 


133 


7 


4548 


4681 


4813 


4946 


5079 


i 5211 


5344 


5476 


5609 


5741 


133 


8 


5874 


6006 


6139 


6271 


6403 


1 6535 


6668 


6800 


6932 


7064 


132 


9 


7196 


7328 


7460 


7592 


7724 


1 7855 


7987 


8119 


8251 


8382 


132 


330 


8514 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


1 


9828 


9959 






















0090 
1400 


0221 
1530 


0353 
1661 


0484 
j 1792 


0615 
1922 


0745 
2053 


0876 
2183 


1007 
2314 


131 
131 


2 


521138 


1269 


3 


2444 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


3616 


130 


4 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4656 4785 


4915 


130 


5 


5045 


5174 


5304 


5434 


5563 


5693 


5822 


5951 6081 


6210 


129 


6 


6339 


6469 


6598 


6727 


6856 


6985 


7114 


7243 7372 


7501 


129 


7 


7630 


7759 


7888 


8016 


8145 


8274 


8402 


8531 8660 


8788 


129 


8 


8917 


9045 


9174 


9302 


9430 


9559 


9687 


9815 9943 






0072 
1351 


128 
128 





530200 1 0328 


0456 


0584 


0712 


1 0840 


0968 


1096 1223 



PROPORTioNAii Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


139 


13.9 


27.8 


41.7 


55.6 


69.5 


83.4 


97.3 


111.2 


125.1 


138 


13.8 


27.6 


41.4 


55.2 


69.0 


82.8 


96.6 


110.4 


124.2 


137 


13.7 


27.4 


41.1 


54.8 


68.5 


82.2 


95.9 


109.6 


123.3 


136 


13.6 


27.2 


40.8 


54.4 


68.0 


81.6 


95.2 


108.8 


122.4 


135 


13.5 


27.0 


40.5 


54.0 


67.5 


81.0 


94.5 


108.0 


121.5 


134 


13.4 


26.8 


40.2 


53.6 


67.0 


80.4 


93.8 


107.2 


120.6 


133 


13.3 


26.6 


39.9 


53.2 


66.5 


79.8 


93.1 


106.4 


119.7 


132 


13.2 


26.4 


39.6 


52.8 


66.0 


79.2 


92.4 


105.6 


118.8 


131 


13.1 


26.2 


89.3 


52.4 


65.5 


78.6 


91.7 


104.8 


117.9 


130 


13.0 


26.0 


89.0 


52.0 


65.0 


78.0 


91.0 


104.0 


117.0 


129 


12.9 


25.8 


38.7 


51.6 


64.5 


77.4 


90.3 


103.2 


116.1 


128 


12.8 


25.6 


38.4 


51.2 


64.0 


76.8 


89.6 


102.4 


115.2 


127 


12 7 


25.4 


38.1 


50.8 


63.5 


70.2 


88.9 


101.6 


114.3 



LOGARITHMS OF NUMBERS. 



445 



No. 340 L. 531.] 



[No. 379 L. 579. 



N. 





1 


2 


S 


4 


5 


6 


7 


8 


9 


Diff. 


340 
1 
2 
3 
4 
5 


531479 
2754 
4026 
5294 
6558 
7819 
9076 


1607 
2882 
4153 
5421 
6685 
7945 
9202 


1734 

3009 
4280 
5547 
6811 
8071 
9327 


1862 
3136 
4407 
5674 
6937 
8197 
9452 


1990 
3264 
4534 

5800 
7063 
8322 
9578 


2117 
3391 
4661 
5927 
7189 
8448 
9703 


2245 
3518 

4787 
6053 
7315 
8574 
9829 


2372 
3645 
4914 
6180 
7441 
8699 
9954 


2500 
3772 
5041 
6306 
7567 
8825 


2627 
3899 
5167 
6432 
7693 
8951 


128 
127 
127 
126 
126 
126 


b 


0079 

laso 

2576 

3820 

5060 
6296 
7529 
8758 
9984 


0204 
1454 
2701 
3944 

5183 
6419 
7652 
8881 


125 


7 
8 
9 

350 
1 
2 
3 
4 


540329 
1579 

2825 

4068 
5307 
6543 

7775 
9003 


0455 
1704 
2950 

4192 
5431 
6666 

7898 
9126 


0580 
1829 
3074 

4316 
5555 
6789 
8021 
9249 


0705 
1953 
3199 

4440 
5678 
6913 
8144 
9371 


0830 
2078 
3323 

4564 
5802 
7036 
8267 
9494 


0955 
2203 
3447 

4688 
5925 
7159 
8389 
9616 


1080 
2327 
3571 

4812 
6049 
7282 
8512 
9739 


1205 
2452 
3696 

4936 

617'2 
7405 
8635 
9861 


125 
125 
124 

124 
124 
123 
123 


0106 
1328 
2547 

3702 
4973 
6182 

7387 
8589 
9787 


123 


5 

6 
7 
8 
9 

360 
1 
2 
3 


550228 
1450 
2668 
3883 
5094 

6303 
7507 
8709 
9907 


0351 
1572 
2790 
4004 
5215 

6423 

7627 
8829 


0473 
1694 
2911 
4126 
5336 

6544 

7748 
8948 


0595 
1816 
3033 
4247 
5457 

6664 

7868 
9068 


0717 
1938 
3155 
4368 
5578 

6785 

7988 
9188 


0840 
2060 
3276 
4489 
5699 

6905 
8108 
9308 


0962 
2181 
3398 
4610 
6820 

7026 
8228 
9428 


1084 
2303 
3519 
4731 
5940 

7146 
8349 
9548 


1206 
2425 

3640 
4852 
6061 

726.' 
8469 
9667 


122 
122 
121 
121 
121 

120 
120 
120 


0026 
1221 
2412 
3600 

4784 
5966 
7144 

8319 
9491 


0146 
1340 
2531 
3718 
4903 
6084 
7202 

8436 
9608 


0265 
1459 
2650 

3837 
5021 
6202 
7379 

8554 
9725 


0385 
1578 
2769 
3955 
5139 
6320 
7497 

8671 
9842 


0504 
1698 
2887 
4074 
5257 
6437 
7614 

8788 
9959 


0624 
1817 
3006 
4192 
5376 
6555 
7732 

8905 


0743 
1936 
3125 
4311 
5494 
6673 
7849 

9023 


0863 
2055 
3244 
4429 
5612 
6791 
7967 

9140 


0982 
2174 
3362 
4548 
5730 
6909 
8084 

9257 


119 


4 
5 
6 

7 
8 
9 

370 
1 


561101 
2293 

3481 
4666 

5848 
7026 

8202 
9374 


119 
119 
119 
118 
118 
118 

117 


0076 
1243 

2407 
3568 
4726 
5880 
7032 
8181 
9326 


0193 
1359 
2523 
3684 
4841 
5996 
7147 
8295 
9441 


0309 
1476 
2639 
3800 
4957 
6111 
7262 
8410 
9555 


0426 
1592 
2755 
3915 
5072 
6226 
7377 
8525 
9669 


117 
117 
116 
116 
116 
115 
115 
115 
114 


2 
3 

4 
5 

6 

7 
8 
9 


570543 
1709 

' 2872 
4031 
5188 
6341 
7492 
8639 


0660 
1825 
2988 
4147 
5303 
6457 
7607 
8754 


0776 
1942 
3104 
4263 
5419 
6572 
7722 
8868 


0893 
2058 
3220 
4379 
5534 
6687 
7836 
8983 


1010 
2174 
3336 
4494 
5650 
6802 
7951 
9097 


1126 
2291 
3452 
4610 
5765 
6917 
8066 
9212 



Proportionax. Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


128 


12.8 


25.6 


38.4 


51.2 


* 64.0 


76.8 


89.6 


102.4 


115.2 


127 


12.7 


25.4 


38.1 


50.8 


63.5 


76.2 


88.9 


101.6 


114.3 


126 


12.6 


25.2 


37.8 


50.4 


63.0 


75.6 


88.2 


100.8 


113.4 


125 


12.5 


25.0 


37.5 


50.0 


62.5 


75.0 


87.5 


100.0 


112.5 


124 


12.4 


24.8 


37.2 


49.6 


62.0 


74.4 


86.8 


99.2 


111.6 


123 


12.3 


24.6 


36.9 


4d.2 


61.5 


73.8 


86.1 


98.4 


110.7 


122 


12 2 


24.4 


36.6 


48.8 


61.0 


73.2 


85.4 


97.6 


109.8 


121 


12.1 


24.2 


36.3 


48.4 


60.5 


72.6 


84.7 


96.8 


108.9 


120 


12.0 


2i.O 


36.0 


48.0 


60.0 


72.0 


ai.o 


96.0 


108.0 


119 


11.9 


23.8 


35.7 


47.6 


59.5 


71.4 


83.3 


95.2 


107.1 



446 



LOGARITHMS OF NUMBERS. 



No. 


380. L. 5 


r9.] 














[N 


D. 414 L, 617. 


N. 





1 


2 


3 


4 


5 


6 


' 


8 


9 


Diff. 


3S0 


579784 


9898 




















0012 
1153 


0126 

1267 


0241 

1381 1 


0355 1 
1495 


0469 
1608 


0583 

1722 


0697 

18.33 


0811 
1950 


114 


1 


580925 


1039 




o 


2063 


2177 


2291 


2404 


2518 1 


2631 


2745 


26dS 297'2 


3085 




3 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 




4 


4331 


4444 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5:348 


113 


5 


54G1 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


63G2 


6475 




6 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7-37'4 


7'436 


7599 




7 


7711 


7823 


7935 


8047 


8160 


8272 


8:384 


8496 


8608 


8720 


112 


8 


8a32 


8944 


9056 


9167 


9279 1 


9391 


9503 


9615 


9726 


9838 




9 


9950 






















0061 
1176 


0173 


0284 
1399 


0396 
1510 


0507 
1 1621 


0619 


0730 
1843 


0842 
1955 


0953 
2066 




390 


591065 


1287 


1732 




1 


2177 


2288 


2399 


2510 


2621 


2732 


284:3 


2954 


3064 


3175 


111 


2 


3286 


3397 


3508 


3618 


3729 


3840 


3950 


4061 


4171 


4282 




3 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 




4 


5496 


5606 


5717 


5827 


5937 


6047 


6157 


6267 


6377 


6487 




5 


6597 


6707 


6817 


6927 


7037 


1 7146 


7256 


7366 


7476 


7586 


110 


6 


7695 


7805 


7914 


802-4 


8134 


1 8243 


a353 


8462 


8572 


8681 




*7 


8791 


8900 


9009 


9119 


9228 


9a37 


9446 


9556 


9665 


9774 




8 


9883 


9992 


















109 


0101 


0210 


C319 


1 0428 


0537 


0646 


0755 


0864 


9 


600973 


1082 


1191 


1299 


1408 


1517 


1625 


1734 


1843 


1951 




400 


2060 


2169 


2277 


2386 


2494 


2803 


2711 


2819 


2928 


3036 




1 


3144 


3253 


3361 


3469 


3577 


3G86 


37-94 


3902 


4010 


4118 


108 


2 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


4982 


5089 


5197 




3 


5305 


5413 


5521 


5G28 


5736 


5844 


5951 


6059 


6166 


6274 




4 


6381 


6489 


6596 


6704 


6811 


6919 


7026 


7133 


7241 


7348 




5 


7455 


7562 


7669 


7777 


7884 


7991 


8098 


8205 


8312 


8419 


107 


6 


8526 


8633 


8740 


8847 


8954 


9061 


9167 


9274 


9381 


9488 




7 


9594 


9701 


9808 


9914 
















0021 
1086 


0328 
1192 


0234 
1298 


0341 
1405 


0447 
1511 


0554 

1617 




8 


610660 


0767 


0873 


0979 




9 


1723 


1829 


1936 


2042 


2148 


2:^54 


2360 


2466 


2572 


2678 


106 


410 


2^'84 


2890 


2996 


3102 


3207 


3313 


3419 


3525 


3630 


3736 




1 


3842 


3947 


4053 


4159 


4264 


4370 


4475 


4581 


4686 


4792 




2 


4897 


5003 


5108 


5213 


5319 


i 5424 


5529 


5634 


5740 


5845 




3 


5950 


6055 


6160 


6265 


6370 


! 6476 


6581 


6686 


6790 


6895 


105 


4 


7000 


7105 


7210 


7315 


7420 


7525 


7629 


7734 


7839 


7943 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


118 


11.8 


23.6 


35.4 


47.2 


59.0 


70.8 


82.6 


94.4 


106.2 


117 


11.7 


23.4 


35.1 


46.8 


58.5 


70.2 


81.9 


93.6 


105.3 


116 


11.6 


23.2 


34.8 


46.4 


58.0 


69.6 


81.2 


92.8 


104.4 


115 


11.5 


23.0 


34.5 


46.0 


57.5 


69.0 


80.5 


92.0 


103.5 


114 


11.4 


22.8 


34.2 


45.6 


57.0 


68.4 


79.8 


91.2 


102.6 


113 


11.3 


22.6 


as. 9 


45.2 


56.5 
56.0 


67.8 


79.1 


90.4 


101.7 


112 


11.2 


22.4 


33.6 


44.8 


67.2 


78.4 


89.6 


100.8 


111 


11.1 


22.2 


33.3 


44.4 


55.5 


66.6 


77.7 


88.8 


99.9 


110 


11.0 


22.0 


as.o 


44.0 


55.0 


66.0 


77.0 


88.0 


99.0 


109 


10.9 


21.8 


32.7 


4:3.6 


54.5 


65.4 


76.3 


87.2 


98.1 


108 


10.8 


21.6 


32.4 


43.2 


54.0 


64.8 


75.6 


86.4 


97.2 


107 


10.7 


21.4 


32.1 


42.8 


53.5 


64.2 


74.9 


85.6 


96.3 


106 


10.6 


21.2 


31.8 


42.4 


53.0 


63.6 


74.2 


&4.8 


95.4 


105 


10.5 


21.0 


31.5 


42.0 


52.5 


63.0 


73.5 


84.0 


94.5 


105 


10.5 


21.0 


31.5 


42.0 


52.5 


63.0 


73.5 


84.0 


94.5 


104 


10.4 


20.8 


31.2 


41.6 


52.0 


62.4 


72.8 


83.2 


93.6 



LOGARITHMS OF NUMBERS. 



447 



No. 415 L. 618.] 



[No. 459 L. 662 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


415 
6 


G18048 
9093 


8153 
9198 


8257 
9302 


8362 
9406 


8466 
9511 


8571 
9615 


8676 
9719 


8780 
9824 


8884 
9928 

0908 
2007 
3042 

4076 

5107 
0135 
7161 
8185 
9206 


8989 

0032 
107'2 
2110 
3146 

4179 
5210 
6238 
7263 

8287 
9308 


105 


7 
8 
9 

420 
1 
2 
3 
4 
5 
6 


620136 
1176 
2214 

3249 

4282 
5312 
6340 
7366 
8389 
9410 


0240 
1280 
2318 

3353 
4385 
5415 
6443 
7468 
8491 
9512 


0344 
1384 
2421 

3456 
4488 
5518 
6546 
7571 
8593 
9613 


0448 
1488 
2525 

3559 
4591 
5621 
6648 
7678 
£695 
9715 


0552 
1592 

2628 

3663 
4695 
5724 
6751 

7775 
8797 
9817 


0656 
1695 
2732 

3766 
4798 
5827 
6853 
7878 
.8900 
9919 

0936 
1951 
2963 

3973 
4981 
5986 
6989 
7990 
8988 
9984 


0760 
1799 

2835 

3869 
4901 
5929 
6956 
7980 
9002 


0864 
1903 
2939 

3973 
5004 
6032 
7058 
8082 
9104 


104 

103 

102 


0021 
1038 
2052 
3064 

4074 
5081 
6087 
7089 
8090 
9088 


0123 
1139 
2153 
3165 

4175 
5182 
6187 
7189 
8190 
9188 


0224 
1241 
2255 
3266 

4276 
5283 

6287 
7290 
8290 
9287 


0326 
1342 
2356 

3367 

4376 

5383 
6388 
7390 

8389 
9387 




7 
8 
9 

430 
1 
2 
3 
4 
5 
6 


630428 
1444 
2457 

3468 

4477 
5484 
6488 
7490 
8489 
9486 


0530 
1545 
2559 

3569 
4578 
5584 
6588 
7590 
8589 
9586 


0631 
1647 
2660 

3670 
4679 
5685 
6688 
7690 
8689 
9686 


0733 

1748 
2761 

3771 
4779 

5785 
6789 
7790 
8789 
9785 


0835 
1849 
2862 

3872 
4880 
5886 
6889 
7890 
8888 
9885 


101 
100 


0084 
1077 
2069 
3058 

4044 
5029 
6011 
6992 
7969 
8945 
9919 


0183 
1177 
2168 
3156 

4143 
5127 
6110 
7089 
8067 
9043 


0283 
1276 
2267 
3255 

4242 
5226 
6208 
7187 
8165 
9140 


0382 
1375 
2366 
3354 

4340 
5324 
6306 
7285 
8262 
9237 




7 
8 
9 

440 
1 
2 
3 
4 
5 
6 


640481 
1474 
2465 

3453 
4439 
5422 
6404 
7383 
8360 
9335 


0581 
1573 
2563 

3551 
4537 
5521 
6502 
7481 
8458 
9432 


0680 
1672 
2662 

3650 
4636 
5619 
6600 
7579 
8555 
9530 


0779 
1771 
2761 

3740 
4734 
5717 
6698 
7676 
8653 
9627 


0879 
1871 
2860 

3847 

4832 
5815 
6796 
7774 
8750 
9724 


0978 
1970 
2959 

3946 
4931 
5913 
6894 

7872 
8848 
9821 


99 

98 


0016 
0987 
1956 
2923 

3888 
4850 
5810 
6769 
7725 
8679 
9631 


0113 
1084 
2053 
3019 

3984 
4946 
5906 
6864 

7820 
8774 
9726 


0210 
1181 
2150 
3116 

4080 
5042 
6002 
6960 
7916 
8870 
9821 




7 
8 
9 

450 
1 
2 
3 
4 
5 
6 
7 


650308 
1278 
2246 

3213 

4177 
5138 
6098 
7056 
8011 
8965 
9916 


0405 
1375 
2343 

3309 
427'3 
5235 
6194 
7152 
8107 
9060 


0502 
1472 
2440 

3405 
4369 
5331 
6290 

7247 
8202 
9155 


0599 
1569 
2536 

3502 
4465 
5427 
6386 
7343 
8298 
9250 


0696 
1666 
2633 

3598 
4562 
5523 
6482 
7438 
8393 
9346 


0793 
1762 
2730 

3695 
4658 
5619 
6577 
7534 
8488 
9441 


0890 
1859 
2826 

3791 
4754 
5715 
6673 

7629 
8584 
9536 


97 
96 


0011 
0960 
1907 


0106 
1055 
2002 


0201 
1150 
2096 


0296 
1245 
2191 


0391 
1339 

2286 


0486 
1434 
2380 


0581 
1529 
2475 


0676 
1623 
2569 


0771 
1718 
2663 


95 


8 
9 


660865 
1813 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


105 


10.5 


2t0 


31.5 


42.0 


52.5 


63.0 


73.5 


84.0 


94.5 


104 


10.4 


20.8 


31.2 


41.6 


52.0 


62.4 


72 8 


83.2 


93.6 


103 


10.3 


20.6 


30.9 


41.2 


51.5 


61.8 


72 1 


82.4 


92.7 


102 


10.2 


20.4 


30.6 


40.8 


51.0 


61.2 


71 4 


81.6 


91.8 


101 


10.1 


20.2 


30.3 


40.4 


50.5 


60.6 


70 7 


80.8 


90.9 


100 


10.0 


20.0 


30.0 


40.0 


50.0 


60.0 


70 


80.0 


90.0 


99 


9.9 


19.8 


29.7 


39.6 


49.5 


59.4 


69.3 


79.2 


89.1 



448 



LOGARITHMS OF NUMBERS. 



No. 460 L. 662.] 




[No. 499 L. 698. 


N 





1 


2 


8 


4 


5 


6 


7 


8 


9 


Diff. 


400 662758 


2852 


2947 


3041 


3135 


3230 


3324 


3418 


3512 


3607 




1 1 3701 


3795 


3889 


3983 


4078 


4172 


4266 


4360 


4454 


4548 




2 1 4642 


4736 


4830 


4924 


5018 


5112 


5206 


5299 


5393 


5487 


94 


3 1 5581 


5675 


5769 


5862 


5956 


6050 


6143 


6237 


6331 


6424 




4 1 G518 


6612 


6705 


6799 


6892 


6986 


7079 


7173 


7266 


7360 




5 ' 7453 


7546 


7640 


7733 


7826 


7920 


8013 


8106 


8199 


8293 




6 


8386 


8479 


857'2 


8665 


8759 


8852 


8945 


9038 


9131 


9224 




ry 


9317 


9410 


9503 


9596 


9689 


9782 


9875 


9967 








i 


0060 

0988 


0153 
1080 


93 


8 


670246 


0339 


0431 


0524 


0617 


0710 


0802 


0895 




9 


1173 


1265 


1358 


1451 


1543 


1636 


1728 


1821 


1913 


2005 




470 


2098 


2190 


2283 


2375 


2467 


2560 


2652 


2744 


2836 


2929 




1 


3021 


3113 


3205 


3297 


3390 


3482 


3574 


3666 


3758 


3850 




2 


3942 


4034 


4126 


4218 


4310 


4402 


4494 


4586 


4677 


4769 


92 


3 


4861 


4953 


5045 


5137 


5228 


5320 


5412 


5503 


5595 


5687 




4 


5778 


5870 


5962 


6053 


6145 


6236 


6328 


6419 


6511 


6602 




5 


6694 


6785 


6876 


6968 


7059 


7151 


7242 


7333 


7424 


7516 




6 


7607 


7698 


7789 


7881 


7972 


, 8063 


8154 


8245 


8336 


8427 




7 


8518 


8609 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


91 


8 


9428 


9519 


9610 


9700 


9791 


i 9882 


9973 










0063 
0970 


0154 
1060 


0245 
1151 




9 


680336 


0426 


0517 


0607 


0698 


0789 


0879 




-©0 


1241 


1332 


1422 


1513 


1603 


1693 


1784 


1874 


1964 


2055 




1 


2145 


2235 


2326 


2416 


2506 


2596 


2686 


2777 


2867 


2957 




2 


3047 


3137 


3227 


3317 


3407 


' 3497 


3587 


3677 


3767 


3857 


90 


3 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 




4 


4845 


4935 


5025 


5114 


5204 


5294 


5383 


5473 


5563 


5652 




5 


5742 


5831 


5921 


6010 


6100 


6189 


6279 


6368 


6458 


6547 




6 


6636 


6726 


€815 


6904 


6994 


7083 


7172 


7261 


7351 


7440 




7 


7529 


7618 


7707 


7796 


7886 


7975 


8064 


8153 


8242 


8331 


89 


6 


8420 


8509 


8598 


8687 


8776 


8865 


8953 


9042 


9131 


9220 




9 


9309 


9398 


9486 


9575 


9664 


9753 


9841 


9930 








0019 
0905 


0107 
0993 




490 


690196 


0285 


0373 


0462 


0550 


0639 


0728 


0816 




1 


1081 


1170 


1258 


1347 


1435 


1524 


1612 


1700 


1789 


1877 




2 


1965 


2053 


2142 


2230 


2318 


2406 


2494 


2583 ! 2671 


2759 




3 


2847 


2935 


3023 


3111 


3199 


3287 


3375 


3463 


S551 


3639 


88 


4 


3727 


3815 


3903 


3991 


4078 


4166 


4254 


4342 


4430 


4517 




5 


4605 


4693 


4781 


4868 


4956 


5044 


5131 


5219 


5307 


5394 




6 


5482 


5569 


5657 


6744 


5832 


5919 


6007 


6094 


6182 


6269 




7 


6356 


6444 


6531 


6618 


6706 


6793 


6880 


6968 


7055 


7142 




8 


7229 


7317 


7404 


7491 


7578 


7665 


7752 


7839 


7926 


8014 




9 


8100 


8188 


8275 


8362 


8449 


8535 


8622 


8709 


8796 


8883 


87 


Proportional Parts. 


Diff. 


1 


2 


3 


• 
4 


5 


6 


7 


8 


9 


98 


9.8 


19.6 


29.4 


i 


J9.2 


49.0 


58.8 


68.6 


78.4 


88.2 


97 


9.7 


19.4 


29.1 


{ 


J8.8 


48.5 


58.2 


67.9 


77.6 


87.3 


96 


9.6 


19.2 


28.8 


i 


J8.4 


48.0 


57.6 


67.2 


76.8 


86.4 


95 


9.5 


19.0 


28.5 


I 


58.0 


47.5 


57.0 


66.5 


76.0 


85.5 


94 


9.4 


18.8 


28.2 


£ 


17.6 


47.0 


56.4 


65.8 


75.2 


84.6 


93 


9.3 


18.6 


27.9 


j^ 


J7.2 


46.5 


55.8 


65.1 


74.4 


83.7 


92 


9.2 


18.4 


27.6 


\ 


6.8 


46.0 


55.2 


64.4 


73.6 


82.8 


91 


9.1 


18.2 


27.3 


S 


6.4 


45.5 


54.6 


63.7 


72.8 


81.9 


90 


9.0 


18.0 


27.0 


g 


6.0 


45.0 


54.0 


63.0 


72.0 


81.0 


89 


8.9 


17.8 


26.7 


a 


15.6 


44.5 


53.4 


62.3 


71.2 


80.1 


88 


8.8 


17.6 


26.4 


a 


S.2 


44.0 


52.8 


61.6 


70.4 


79.2 


87 


8.7 


17.4 


26.1 


a 


;4.'8 


48.5 


-52.2 


•60.9 


69.6 


78 .-3 


86 


8.6 


17.2 


25.8 


a 


4.4 43.0 


51.6 


60.2 


68.8 


77.4 



LOGARITHMS OF KTTMBERS. 



449 



No. 


500 L. 698.] 














[N 


0. 544 L. 736. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


500 
1 


698970 

9838 


9057 
9924 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


9751 




0011 
0877 
1741 
2603 
3463 
4322 
5179 
6035 
6888 

7740 
8591 
9440 


0098 
0963 
1827 
2689 
3549 
4408 
5265 
6120 
6974 

7826 
8676 
9524 


0184 
1050 
1913 
2775 
3635 
4494 
5350 
6206 
7059 

7911 
8761 
9609 


0271 
1136 
1999 
2861 
3721 
4579 
5436 
6291 
7144 

7996 
8846 
9694 


0358 
1222 
2086 
2947 
3807 
4665 
5522 
6376 
7229 

8081 
8931 
9779 


0444 
1309 
2172 
3033 
3893 
4751 
5607 
6462 
7315 

8166 
9015 
9863 


0531 
1395 

2258 
3119 
3979 
4837 
5693 
6547 
7400 

8251 
9100 
9948 


0617 

1482 
2344 

3205 
4065 

4922 
5778 
6632 

7485 

8336 
9185 




2 
3 

4 
5 
6 

7 
8 
9 

510 
1 
2 


700704 
1568 
2431 
3291 
4151 
5008 
5864 
6718 

7570 
8421 
9270 


0790 
1654 
2517 
3377 
4236 
5094 
5949 
6803 

7655 
8506 
9355 


86 
85 


0033 
0879 
1723 
2566 
3407 
4246 
5084 
5920 

6754 

7587 
8419 
9248 




3 

4 
5 
6 
7 
8 
9 

520 
1 
2 
3 
4 


710117 
0963 
1807 
2650 
3491 
4330 
5167 

6003 
6838 
7671 
8502 
9331 


0202 
1048 
1892 
2734 
3575 
4414 
5251 

6087 
6921 
7754 
8585 
9414 


0287 
1132 
1976 
2818 
3659 
4497 
5335 

6170 
7004 

7837 
8668 
9497 


0371 
1217 
2060 
2902 
3742 
4581 
5418 

6254 

7088 
7920 
8751 
9580 


0456 
1301 

2144 
2986 
3826 
4665 
5502 

6337 
7171 

8003 

8834 
9663 


0540 
1385 
2229 
3070 
3910 
4749 
5586 

6421 
7254 

8086 
8917 
9745 


0625 
1470 
2313 
3154 
3994 
4833 
5669 

6504 

7338 
8169 
9000 

9828 


0710 
1554 
2397 
3238 
4078 
4916 
5753 

6588 
7421 
8253 
9083 
9911 


0794 
1639 
2481 
3323 
4162 
5000 
5836 

6671 
7504 
8336 
9165 
9994 


84 
83 


0077 
0903 
1728 
2552 
3374 
4194 

5013 
5830 
6646 
7460 

8273 
9084 
9893 




5 
6 

7 
8 
9 

530 
1 
2 
3 
4 
5 
6 


720159 
0986 
1811 
2634 
3456 

4276 
5095 
5912 
6727 
7541 
8354 
9165 
9974 


0242 
1068 
1893 
2716 
3538 

4358 
5176 
5993 
6809 
?623 
8435 
9246 


0325 
1151 
1975 
2798 
3620 

4440 
5258 
6075 
6890 
7704 
8516 
9327 


0407 
1233 

2058 
2881 
3702 

4522 
5340 
6156 
6972 
7785 
8597 
9408 


0490 
1316 
2140 
2963 

37'84 

4604 
5422 
6238 
7053 
7866 
8678 
9489 


0573 
1398 
2222 
3045 
3866 

4685 
5503 
6320 
7134 
7948 
8759 
9570 


0655 

1481 
2305 
3127 
3948 

4767 

5585 
6401 
7216 
8029 
8841 
9651 


0738 
1563 
2387 
3209 
4030 

4849 
5667 
6483 
7297 
8110 
8922 
9732 


0821 
1646 
2469 
3291 
4112 

49bl 

5748 
6564 
7379 
8191 
9008 
9813 


82 
81 


0055 
0863 
1669 

2474 

3278 
4079 
4880 
5679 


0136 
0944 
1750 

2555 
3358 
4160 
4960 
5759 


0217 
1024 
1830 

2635 
3438 
4240 
5040 
5838 


0298 
1105 
1911 

2715 
3518 
4320 
5120 
5918 


0378 
1186 
1991 

2796 
3598 
4400 
5200 
5998 


0459 
1266 

2072 

2876 
3679 
4480 
5279 
6078 


0540 
1347 

2152 

2956 
3759 
4560 
5359 
6157 


0621 
1428 
2233 

3037 
3839 
4640 
5439 
6237 


0702 
1508 
2313 

3117 
3919 
4720 
5519 
6317 




8 
9 

540 
1 
2 
3 
4 


730782 
1589 

2394 
8197 
3999 
4800 
5599 


80 



Proportional Parts. 



Diff. 


1 
8.7 


2 


3 


4 


5 


6 


7 


8 


9 


87 


17.4 


26.1 


34.8 


43.5 


52.2 


60 9 


69.6 


78.3 


E(j 


8.6 


17.2 


25.8 


34.4 


43.0 


51.6 


60.2 


68.8 


77.4 


m 


8.5 


17.0 


25.5 


34.0 


42.5 


51.0 


59.;) 


68.0 


76.5 


84 


8.4 


16.8 


25.2 


33.6 


42.0 


50.4 


58.8 


67.2 


75.6 



450 



LOGARITHMS OF NUMBERS. 



No. 


545 L. 736.] 














IN 


D. 5841 


.. 767. 
Diff. 


N. 


12 


3 


4 


^ 


6 


7 


8 9 1 


545 


736397 ' 6476 ; 


6556 6635 6715 


6795 


6874 


6954 


7034 7113 




6 


7193 7272 


7352 7431 7511 


7590 


7670 


7749 


7829 i 7908 




7 


7987 : 8067 


8146 8225 8305 


8384 


8463 


8543 


8622 8701 




8 


8781 8860 


8939 


9018 9097 


9177 


9256 


9335 


9414 , 9493 




9 


9572 


9651 i 


9731 


9810 9889 ; 


9968 










0047 
0836 


0126 
0915 


0205 0284 
0994 1073 


79 


550 


740363 


0442 ^ 0521 


0600 0678 ^ 


0757 


1 


1152 


1230 1309 


1388 1467 


1546 


1624 


1703 


1782 1860 




2 


1939 


2018 i 2096 


2175 I 2254 


2332 


2411 


2489 


2568 


2647 




3 


2725 


2804 1 2882 


2961 1 3039 : 


3118 


3196 


3275 


3353 


3431 




4 


3510 


3588 3667 


3745 ! 3823 


3902 


3980 


4058 


4136 


4215 




5 


4293 


4371 i 4449 


4528 4606 


4684 


4762 


4840 


4919 


4997 




6 


5075 


5153 5231 


5309 5387 


5465 


5543 


5621 


5699 


5777 


78 


7 


5855 


5933 1 6011 


6089 6167 


1 6245 


6323 


6401 


6479 


6556 




8 


6634 


6712 6790 


6868 i 6945 


7023 


7101 


7179 


7256 


7334 




9 


7412 


7489 


7567 


7645 7722 


: 7800 


7878 


7955 


8033 


8110 




560 


8188 


8266 


8343 


8421 8498 


8576 


8653 


8731 


8808 


8885 




1 


8963 


9040 i 91J8 


9195 9272 


9350 


9427 


9504 


9582 


9659 




2 


9736 


9814 I 9891 


9968 














nnAK 


0123 
0894 


0200 
0971 


0277 
1048 


0354 
1125 


0431 
1202 




3 


750508 


0586 , 0663 0740 0817 




4 


1279 


1356 i 1433 1510 1587 


1604 


1741 


1818 


1895 


1972 


77 


5 


2048 


2125 1 2202 1 2279 i 2356 


2433 


2509 


2586 


2663 


2740 


6 


2816 


2893 ' 2970 ! 3047 | 3123 


3200 


3277 


3353 


3430 


3506 




7 


3583 


3660 3736 3813 3889 


3966 


4042 


4119 


4195 


4272 




8 


4348 


4425 1 4501 i 4578 \ 4654 


i 4730 


4807 


4883 


4960 


50:^6 




9 


5112 


5189 


5265 


5341 5417 


5494 


5570 


5646 


5722 


5799 




570 


5875 


5951 


6027 


6103 6180 


^ 6256 


6332 


6408 


6484 


6560 




1 


6636 


6712 


6788 


, 6864 i 6940 


7016 


7092 7168 


7244 


7320 


76 


2 


7396 


7472 [ 7548 [ 7624 \ 7700 


7775 


7851 ! 7927 


8003 


8079 




3 


8155 


8230 8306 ! 8382 8458 


8533 


8609 8685 


8761 


8836 




4 


8912 


8988 9063 , 9139 9214 


9290 


9366 1 9441 


9517 


9592 




5 


9668 


QTAR 1 Q81Q 1 QftQl ' 0070 
















0045 
0799 


0121 1 0196 
0875 1 0950 


0272 
1025 


0347 
1101 




6 


760422 


0498 0573 0649 


0724 




7 


1176 


1251 1326 1402 


1477 


1552 


1627 ' 1702 


1778 


1853 




8 


1928 


2003 


2078 2153 


2228 


2303 


2378 ' 2453 


2529 


2604 


73 


9 


2679 


2754 


2829 2904 


2978 


3053 


3128 I 3203 


3278 


3353 


580 


3428 


3503 


3578 3653 


3727 


3802 


3877 


3952 


4027 


4101 




1 


4176 


4251 


4326 4400 


4475 


4550 


4624 


4699 


; 4774 


4848 




2 


4923 


4998 


5072 


5147 


5221 


i 5296 


5370 


5445 


5520 


5594 




3 


5669 


5743 


5818 


5892 


5966 


' 6041 


6115 


6190 


6264 


6338 




4 


6413 


6487 


6562 


6636 


6710 


6785 


6859 


6933 


7007 


7082 





Proportional Parts. 



Difif. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


as 


8.3 


16.6 


24.9 


33.2 


41.5 


49.8 


58.1 


66.4 


74 7 


82 


8.2 


16.4 


24.6 


32.8 


41.0 


49.2 


57.4 


65.6 


73 b 


81 


8.1 


16.2 


24.3 


32.4 


40.5 


48.6 


56.7 


64.8 


72 i 


80 


8.0 


16.0 


24.0 


32.0 


40.0 


48.0 


56.0 


64.0 


72 C 


79 


7.9 


15.8 


23.7 


31.6 


39.5 


47.4 


55.3 


63.2 


71 1 


78 


7.8 


15.6 


23.4 


31.2 


39.0 


46.8 


54.6 


62.4 


70 ^ 


77 


7.7 


15.4 


2:^.1 


30.8 


38.5 


46.2 


53.9 


61.6 


69 c 


76 


7.6 


15.2 


22.8 


30.4 


38.0 


45.6 


53.2 


60.8 


68 4 


75 


7.5 


15.0 


22.5 


30.0 


37.5 


45.0 


52.5 


60.0 


67 t 


74 


7.4 


14.8 


22.2 


29.6 


37.0 


44.4 


51.8 


59.2 


m t 



LOGARITHMS OF NUMBERS. 



451 



lio. 585L. 767.] 










[No. 629 L. 799. 


5^ 





1 


2 


3 


i 


5 


6 


7 


8 


9 


Diff. 


767156 


7230 


7304 


7379 


7453 


7527 


7601 


7675 


7749 


7823 




6 


7898 


7972 


8046 


8120 


8194 


8268 


8342 


8416 


8490 


8564 


74 


7 


8638 


8712 


8786 


8860 


8934 


9008 


9082 


9156 


9230 


9303 




8 


9377 


9451 


9525 


9599 


9673 


9746 


9820 


9894 


9968 






0042 
0778 




9 


770115 


0189 


0263 


0336 


0410 


0484 


0557 


0631 


0705 




590 


0852 


0926 


0999 


1073 


1146 


1220 


1293 


1367 


1440 


1514 




1 


1587 


1661 


1734 


1808 


1881 


1955 


2028 


2102 


2175 


2248 




2 


2322 


2395 


2468 


2542 


2615 


2688 


2762 


2835 


2908 


2981 




3 


3055 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 




4 


3786 


3860 


3933 


4006 


4079 


4152 


4225 


4298 


4371 


4444 


73 


5 


4517 


4590 


4663 


4736 


4809 


4882 


4955 


5028 


5100 


5173 




6 


5246 


5319 


5392 


5465 


5538 


5610 


5683 


5756 


5829 


5902 




7 


5974 


6047 


6120 


6193 


6265 


6338 


6411 


6483 


6556 


6629 




8 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7354 




9 


7427 


7499 


7572 


7644 


7717 


7789 


7862 


7934 


8006 


8079 




600 


8151 


8224 


8296 


8368 


8441 


8513 


8585 


8658 


8730 


8802 




1 


8874 


8947 


9019 


9091 


9163 


9236 


9308 


9380 


9452 


9524 




2 


9596 


9669 


9741 


9813 


9885 


9957 












0029 


0101 

0821 


0173 
0893 


9245 
0965 




3 


780317 


0389 


0461 


0533 


0605 


0677 


0749 


72 


4 


1037 


1109 


1181 


1253 


1324 


1396 


1468 


1540 


1612 


1684 




6 


1755 


1827 


1899 


1971 


2042 


2114 


2186 


2258 


2329 


5401 




6 


2473 


2544 


2616 


2688 


2759 


2831 


2902 


2974 


3046 


3117 




7 


3189 


3260 


3332 


3403 


3475 


3546 


3618 


3689 


3761 


3832 




8 


3904 


3975 


4046 


4118 


4189 


4261 


4332 


4403 


4475 


4546 




9 


4617 


4689 


4760 


4831 


4902 


4974 


5045 


5116 


5187 


5259 




610 


5330 


5401 


5472 


5543 


5615 


5686 


5757 


5828 


5899 


5970 




1 


6041 


6112 


6183 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


71 


2 


6751 


6822 


6893 


6964 


7035 


71 u6 


7177 


7248 


7319 


7390 




3 


7460 


7531 


7602 


7673 


7744 


78i5 


7885 


7956 


8027 


8098 




4 


8168 


8239 


8310 


8381 


8451 


8522 


8593 


8663 


8734 


8804 




5 


8875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


9510 




6 


9581 


9651 


9722 


9792 


9863 


9933 






















0004 
0707 


0074 

0778 


0144 

0848 


0215 
0918 




7 


790285 


0356 


0426 


0496 


0567 


0637 




8 


0988 


1059 


1129 


1199 


1269 


1340 


1410 


1480 


1550 


1620 




9 


1691 


1761 


1831 


1901 


1971 


2041 


2111 


2181 


2252 


2322 




620 


2392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


1 


3092 


3162 


3231 


3301 


3371 


3441 


3511 


3581 


3651 


3721 




2 


3790 


3860 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 




3 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5045 


5115 




4 


5185 


5254 


5324 


5393 


5463 


5532 


5602 


5672 


5741 


5811 




5 


5880 


5949 


6019 


6088 


6158 


6227 


6297 


6366 


6436 


6505 




6 


6574 


6644 


6713 


6782 


6852 


6921 


6990 


7060 


7 (29 


7198 




7 


7268 


7337 


7406 


7475 


7545 


7614 


7683 


7752 


7821 


7890 




8 


7960 


8029 


8098 


8167 


8236 


8305 


8374 


8443 


8513 


8582 




9 


8651 


8720 


8789 


8858 


8927 


8996 


9065 


9134 


9203 


9272 


69 


Proportional Parts. 


Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


75 


7.5 


15.0 


22 


.5 




30.0 


37.5 


45.0 


5^ 


J. 5 


60.0 


67.5 


74 


7.4 


14.8 


22 


.2 




29.6 


37.0 


44.4 


51 


.8 


59.2 


66.6 


73 


7.3 


14.6 


21 


.9 




29.2 


36.5 


43.8 


51 


.1 


58.4 


65.7 


72 


7.2 


14.4 


21 


.6 


28.8 


36.0 


43.2 


5( 


).4 


57.6 


64.8 


71 


7.1 


14.2 


21 


.3 


28.4 


35.5 


42.6 


4f 


).7 


56.8 


63.9 


70 


7.0 


14.0 


21 


.0 


28.0 


35.0 


42.0 


41 


).0 


56.0 


63.0 


6d 


6.9 


13.8 


20 


.7 


27.6 


34.5 


41.4 


4^ 


i.3 


55.2 


62.1 



452 



LOGARITHMS Of NfMBERS. 



No. 630 L, 799.] 










[No. 674 L. 829. ] 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


630 

1 


799341 


9409 


9478 


9547 


9616 1 


9685 


9754 


9823 


9892 


9961 




800029 


0098 


0167 


0236 


0305 


0373 


0442 


0511 


0580 


0648 


2 


0717 


0786 


0854 


0923 


0992 


1061 


1129 


1198 


1266 


1335 




3 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 




4 


2089 


2158 


2226 


2295 


2363 


2432 


2500 


2568 


2637 


2705 




5 


2774 


2842 


2910 


2979 


3047 


3116 


3184 


8252 


3321 


3389 




6 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


4071 




7 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4616 


4685 


4753 




8 


4821 


4889 


4957 


5025 


5093 


5161 


5229 


5297 


5365 


5433 


68 


9 


5501 


5569 


5637 


5705 


5773 


5841 


5908 


5976 


6044 


6112 




640 


806180 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 




1 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 




2 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8143 




3 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 




4 


8886 


8953 


9021 


9088 


9156 


9223 


9290 


9358 


9425 


9492 




5 


9560 


9627 


9694 


9762 


9829 


9896 


9964 






















0031 
0703 


0098 
0770 


0165 

0837 




6 


810233 


0300 


0367 


0434 


0501 


0569 


0636 




7 


0904 


0971 


1039 


1106 


1173 


1240 


1307 


1374 


1441 


1508 


67 


8 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 




9 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 




650 


2913 


2980 


3047 


3114 


3181 


3247 


3314 


3381 


3448 


3514 




1 


3581 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


4114 


4181 




2 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 




3 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


5511 




4 


5578 


5644 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 




5 


6241 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 




6 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 




7 


7565 


7631 


7698 


7764 


7830 


7896 


7962 


8028 


8094 


8160 




8 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


9 
660 


8885 
9544 


8951 
9610 


9017 
9676 


9083 
9741 


9149 

9807 


9215 

9873 


9281 
9939 


9346 


9412 


9478 
























0004 
0661 


0070 
0727 


0136 
0792 




1 


820201 


0267 


0333 


0399 


0464 


0530 


0595 




2 


0858 


0924 


0989 


1055 


1120 


1186 


1251 


1317 


1382 


1448 




3 


1514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 




4 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 




5 


2822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 




6 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 




7 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


4581 


4646 


4711 


65 


8 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


9 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 




670 


6075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 




1 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


7305 




2 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 




3 


8015 


8080 


8144 


8209 


8273 


8338 


&402 


&467 


8531 


8595 




4 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 




Proportional Parts. 


Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


68 


6.8 


13.6 


20 


4 




J7.2 


34.0 


40.8 




47 


.6 




54.4 


61.2 


67 


6.7 


13.4 


20 


1 




26.8 


33.5 


40.2 




46 


.9 




53.6 


60.3 


66 


6.6 


13.2 


19 


8 




J6.4 


33.0 


39.6 




46 


.2 




52.8 


59.4 


65 


6.5 


13.0 


19 


5 




26.0 


32.5 


39.0 




45 


.5 




52.0 


58.5 


64 


6.4 


1£.8 


19 


2 




25.6 


32.0 


38.4 




44 


.8 




51.2 


57.6 



LOGARITHMS OF KUMBERS. 



453 



No. 


675 L. 829.] 














[No. 719 L. 857. 


N. 





1 


2 


S 


4 


5 


6 


7 


8 


9 


Diff 


675 


829304 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 




6 


9947 






















0011 
0653 


0075 
0717 


0139 

0781 


0204 
0845 


0268 
0909 


0332 

0973 


0396 
1037 


0460 
1102 


0525 
1166 




7 


830589 




8 


1230 


1294 


1358 


1422 


1486 


1550 


1614 


1678 


1742 


1806 


64 


9 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 




680 


2509 


2573 


2637 


2700 


2764 


2828 


2892 


?956 


3020 


3083 




1 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 




2 


3784 


3848 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357 




3 


4421 


4484 


4548 


4611 


4675 


4739 


4802 


4866 


4929 


4993 




4 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 




5 


6691 


5754 


5817 


5881 


5944 


6007 


6071 


6134 


6197 


6261 




6 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6830 


6894 




7 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 




8 


7588 


7652 


7715 


7778 


7841 


7904 


7967 


8030 


8093 


8156 




9 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 


63 


690 


8849 


8912 


8975 


9038 


9101 


9164 


9227 


9289 


9352 


9415 




J 


9478 


9541 


9604 


9667 


9729 


9792 


9855 


9918 


9981 








0043 
0671 




2 


840106 


0169 


0232 


0294 


0357 


(yi20 


0482 


0545 


0608 




3 


0733 


0796 


0859 


0921 


0984 


1046 


1109 


1172 


1234 


1297 




4 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


1860 


1922 




5 


1985 


2047 


2110 


2172 


2235 


2297 


2360 


2422 


2484 


2547 




6 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


3108 


3170 




7 


3233 


3295 


3357 


3120 


34S2 


3544 


3606 


3669 


3731 


3793 




8 


3855 


3918 


3980 


4042 


4104 


4166 


4229 


4291 


4353 


4415 




9 


4477 


4539 


4601 


4664 


4726 


4788 


4850 


4912 


4974 


5036 




700 


5098 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


62 


1 


5718 


5780 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 




2 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 




3 


6955 


7017 


7079 


7141 


7202 


7264 


7326 


7388 


7449 


7511 




4 


7573 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 




5 


8189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 




6 


8805 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 




7 


9il9 


9481 


9542 


9604 


9665 


9726 


9788 


9849 


9911 


9972 




8 


850033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


0585 




9 


0646 


0707 


0769 


0830 


0891 


0952 


1014 


1075 


1136 


1197 




710 


1258 


1330 


1381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 




1 


1870 


1931 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 




2 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


3 


3090 


3150 


3211 


3272 


3333 


3394 


3455 


3516 


3577 


3637 




4 


3698 


3759 


3820 


3881 


3941 


4002 


4063 


4124 


4185 


4245 




5 


4306 


4367 


4428 


4488 


4549 


4610 


4670 


4731 


4792 


4852 




6 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 




7 


5519 


5580 


5640 


5701 


5761 


5822 


5882 


5943 


6003 


6064 


8 


6124 


6185 


6245 


6306 


6366 


6427 


6487 


6548 


6608 


6668 


9 


6729 


6789 


6850 


6910 


6970 


7031 


7091 


7152 


7212 


7272 





Proportional Parts. 



Diff. 

65 
64 
63 
62 
61 
60 



6.5 
6.4 
6.3 
6.2 
6.1 
6.0 I 



13.0 
12.8 
12.6 
12.4 
12.2 
12.0 



19.5 
19.2 
18.9 
18.6 
18.3 
18.0 



26.0 
25.6 
25.2 
24.8 
24.4 
24.0 



32.5 
32.0 
31.5 
31.0 
30.5 
30.0 



39.0 
38.4 
37.8 
37.2 
36.6 
36.0 



45.5 

44.8 
44.1 
43.4 

42.7 
42.0 



52.0 
51.2 
50.4 
40.6 

48.8 
48.0 



9 

58.5 
57.6 
56.7 
55.8 
54.9 
54.0 



454 



LOGARITHMS OP NUMBERS. 



No. 


720 L. 857.] 














[No. 704 L. 883. 


N. 





1 2 


3 


4 


6 


6 


7 


8 


9 


Diff. 


720 


857332 


7393 


7453 


7513 


7574 


7634 


7694 


7755 


7815 


7875 




1 


7935 


7995 


8056 


8116 


8176 


8236 


8297 


8357 


8417 


8477 




2 


8537 


8597 


8657 


8718 


8778 


8838 


8898 


8958 


9018 


9078 




3 


9138 


9198 


9258 


9318 


9379 


9439 


9499 


9559 


9619 


9679 


60 


4 


9739 


9799 


9859 


9918 


9978 














0038 
0637 


0098 


0158 


0218 
0817 


0278 
0877 




5 


860338 


0398 


0458 


0518 


0578 


0697 


0757 




6 


0937 


0996 


1056 


1116 


1176 


1236 


1295 


1355 


1415 


1475 




7 


1534 


1594 


1654 


1714 


1773 


1833 


1893 


1952 


2012 


2072 




8 


2131 


2191 


2251 


2310 


2370 


2430 


2489 


2549 


2608 


2668 




9 


2728 


2787 


2847 


2906 


2966 


3025 


3085 


3144 


3204 


3263 




730 


3323 


3382 


3442 


3501 


3561 


3620 


3680 


3739 


3799 


3858 




1 


3917 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 




2 


4511 


4570 


4630 


4689 


4748 


4808 


4867 


4926 


4985 


5045 




3 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


5519 


5578 


5637 




4 


5696 


5755 


5814 


5874 


5933 


5992 


6051 


6110 


6169 


6228 




5 


6287 


6346 


6405 


6465 


6524 


6583 


C642 


6701 


6760 


6819 




6 


6878 


6937 


6996 


7055 


7114 


7173 


7232 


7291 


7350 


7409 


59 


7 


7467 


7526 


7585 


7644 


7703 


7762 


7821 


7880 


7939 


7998 




8 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8586 




9 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9056 


9114 


9173 




740 


9232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 




1 


9818 


9877 


9935 


9994 
















0053 
0638 


0111 
0696 


0170 
0755 


0228 
0813 


0287 
0872 


0345 
0930 




2 


870404 


0462 


0521 


0579 




3 


0989 


1047 


1106 


1164 


1223 


1281 


1339 


1398 


1456 


1515 




4 


1573 


1631 


1690 


1748 


1806 


1865 


1923 


1981 


2040 


20G8 




5 


2156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 




6 


2739 


2797 


2855 


2913 


2972 


3030 


3088 


8146 


3204 


3262 




7 


3321 


3379 


3437 


3495 


3553 


3611 


3669 


3727 


3785 


3844 




8 


3902 


3960 


4018 


4076 


4134 


4192 


4250 


4308 


4366 


4424 


58 


9 


4482 


4540 


4598 


4656 


4714 


1 4772 


4830 


4888 


4945 


5003 




750 


5061 


5119 


5177 


5235 


5293 


5351 


5409 


5466 


5524 


5582 




1 


5640 


5698 


5756 


5813 


5871 


5929 


5987 


6045 


6102 


6160 




2 


6218 


6276 


6333 


6391 


6449 


6507 


6564 


6622 


6680 


6737 




3 


6795 


6853 


6910 


6968 


7026 


7083 


7141 


7199 


7256 


7314 




4 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 




5 


7947 


8004 


8062 


8119 


8177 


8234 


8292 8349 


8407 


8464 




6 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 




7 


9096 


9153 


9211 


9268 


9325 


9383 


9440 


9497 


9555 


9612 




8 


9669 


9726 


9784 


9841 


9898 


9956 












0013 


0070 


0127 


0185 
0756 




9 


880242 


0299 


0356 


0413 


0471 


0528 


0585 


0642 


0699 




760 


0814 


0871 


0928 


0985 


1042 


1099 


1156 


1213 


1271 


1328 




1 


1385 


1442 


1499 


1556 


1613 


1670 


1727 


1784 


1841 


1898 


57 


2 


1955 


2012 


2069 


2126 


2183 


2240 


2297 


2354 


2411 


2468 


3 


2525 


2581 


2638 


2695 


8752 


2809 


2866 


2923 


2980 


3037 




4 


3093 


3150 


3207 3264 


3321 


3377 


3434 


3491 3548 


3605 





Proportional Parts. 



Diff. 


1 


2 


3 


* 


5 


6 


7 


8 


9 


59 


5.9 


11.8 


17.7 


23.6 


29.5 


35.4 


41.8 


47.2 


53.1 


58 


5.8 


11.6 


17.4 


23.2 


29.0 


34.8 


40.6 


46.4 


52.2 


57 


5.7 


11.4 


17.1 


22.8 


28.5 


34.2 


39.9 


45.6 


51.3 


50 


5.0 


11.2 


16.8 


22.4 


28.0 


3?. 6 


39.2 


44.8 


50.4 



LOGARITHMS OF NUMBEES. 



455 



No. 765 L. 883.] 














[No. 809 L. 908. 


N. 
765 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


883661 


3718 


3775 


3832 


3888 


3945 


4002 


4059 


4115 


4172 


6 


4229 


4285 


4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 




7 


4^95 


4852 


4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 




8 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 




9 


5926 


5983 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 




770 


6491 


6547 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 




1 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


7561 




2 


7617 


7674 


7730 


7786 


7842. 


7898 


7955 


8011 


8067 


8123 




3 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 




4 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 




5 


9302 


9358 


9414 


9470 


9526 


9582 


9038 


9694 


9750 


9806 


56 


6 


9862 


9918 


9974 


















0030 
0589 


0086 
0645 


0141 
0700 


0197 
0756 


0253 
0812 


0309 
0868 


0365 
0924 




7 


890421 


0477 


0533 




8 


0980 


1035 


1091 


1147 


1203 


1259 


1314 


1370 


1426 


1482 




9 


1537 


1593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 




780 


2095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 




1 


2661 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 




2 


3207 


3262 


3318 


3373 


3429 


3484 


3540 


3595 


3651 


3706 




3 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 




4 


4^316 


4371 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 




5 


4870 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 




6 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5809 


5864 


5920 




7 


5975 


6030 


6085 


6140 


6195 


6251 


6306 


6361 


6416 


6471 




8 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 




9 


7077 


7132 


7187 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


55 


790 


7627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


1 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 




2 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 




3 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 




4 


9821 


9875 


9930 


9985 
















0039 
0586 


0094 
0640 


0149 
0695 


0203 
0749 


0258 
0804 


0312 

0859 




5 


900367 


0422 


0476 


0531 




6 


0913 


0968 


1022 


1077 


1131 


1186 


1240 


1295 


1349 


1404 




7 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1^8 




8 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 




9 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 




800 


3090 


3144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 




1 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 




2 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 




3 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


54 


4 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


5 


5796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 




6 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 




7 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


7304 


7358 




8 


7411 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 




9 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 




Proportional Parts. 


Difif. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


57 


5.7 


11.4 




17 


.1 




22.8 


28.5 


34.^ 


J 


3J 


).9 


45.6 


51.3 


56 


5.6 


11.2 




16 


.8 




22.4 


28.0 


33. ( 


1 


31 


).2 


44.8 


50.4 


55 


5.5 


11.0 




16 


.5 




22.0 


27.5 


33. ( 


) 


3^ 


i.5 


44.0 


49.5 


54 


5.4 


10.8 




16 


.2 




21.6 


27.0 


32.^ 


[ 


3'- 


r.8 43.2 


48.6 



456 



LOGARITHMS OF KUMBERS. 



No. 810 L. 908.] 



lNo. 854 L. 931. 



N. 



810 
1 



3 
4 
5 
6 

7 
8 
9 

820 
1 
2 
3 
4 
5 
6 
7 
8 
9 

830 
1 

2 
3 
4 
5 
6 
7 
8 
9 

840 
1 
2 
3 
4 
5 
6 
7 
8 
9 

850 
1 



908485 
9021 
9556 



910091 
0624 
1158 
1690 
2222 
2753 
3284 

3814 
4343 

4872 
5400 
5927 
6454 
6980 
7506 
8030 
8555 

9078 
9601 



920123 
0645 
1166 
1686 
2206 
2725 
3244 
3762 

4279 
4796 
5312 

5828 
6342 
6857 
7370 
7883 
8396 
8908 

9419 
9930 



930440 
0949 
1458 



8539 
9074 
9610 



0144 
0678 
1211 
1743 
2275 
2806 
3337 

3867 
4396 
4925 
5453 
5980 
6507 
7033 
7558 
8083 
8607 

9130 
9653 



0176 
0697 
1218 
1738 
2258 
2777 
3296 
3814 

4331 

4848 
5364 
5879 
6394 
6908 
7422 
7935 
8447 
8959 

9470 
9981 



0491 
1000 
1509 



9128 
9663 



0197 
0731 
1264 
1797 
2328 
2859 
3390 

3920 
4449 
4977 
5505 
6033 
6559 
7085 
7611 
8135 
8659 

9183 
9706 



0228 
0749 
1270 
1790 
2310 
2829 
3348 
3865 

4383 
4899 
6415 
5931 
6445 
6959 
7473 
7986 
8498 
9010 

9521 



9181 
9716 



0251 
0784 
1317 
1850 
2381 
2913 
3443 



8699 8753 
9235 i 9289 
9770 ' 9823 



3973 


4026 


4502 


4555 


5030 


5083 


5558 


5611 


6085 


6138 


6612 


6664 


7138 


7190 


7663 


7716 



8712 

9235 

9758 



0032 
0542 
1051 
1560 



0280 
0801 
1322 
1842 
2362 
2881 
3399 
3917 

4434 
4951 
5467 
5982 
6497 
7011 
7524 
8037 
8549 
9061 

9572 

0083 
0592 
1102 
1010 



0304 
0838 
1371 
1903 
2435 
2966 
3496 



8240 
8764 



0358 
0891 
1424 
1956 
2488 
3j19 
3549 

4079 
4608 
5136 
5664 
6191 
6717 
7243 
7768 
8293 



9340 



9810 ! 9862 



0332 
0853 
1374 
1894 
2414 
2933 
3451 
3969 

4486 
5003 
5518 
6034 
6548 
7062 
7576 
8088 
8601 
9112 



0134 
0643 
1153 
1661 



0384 
09G6 
1426 
1946 
2466 
2985 
3503 
4021 

4538 
5054 
5570 
6085 
6600 
7114 
7627 
8140 
8652 
9163 

9674 



• 0185 
0694 
1204 

I 1712 



9342 

9877 



0411 
0944 
1477 
2009 
2541 
3072 
3602 

4132 
4660 
5189 
5716 
6243 
6770 
7295 
7820 
8345 



8914 
9449 



0518 
1051 
1584 
2116 
2647 
3178 



6296 

t822 
7348 
7873 
8397 
8921 

9392 9444 



0464 
0998 
1530 
2063 
2594 
3125 
3655 

4184 4237 
4713 4766 
5241 , 5294 
5769 i 5822 
6349 
6875 
7400 
7925 
8450 
8973 



9496 



04S6 
C958 
1478 
1998 
2518 
3037 
3555 
4072 

4589 
51-06 
5621 
6137 
6651 
7165 
7678 
8191 
8703 
9215 

9725 



0236 
0745 
1254 
1763 



0489 
1010 
1530 
2050 
2570 
3089 
3607 
4124 

4641 
5157 
5673 
6188 
6702 
7216 
7730 
8242 
8754 
9266 

9776 



0019 
0541 
1062 
1582 
2102 
2622 
3140 
3658 
4176 

4693 
5209 
5725 
6240 
6754 
7268 
7781 
8293 
8805 
9317 

9827 



0287 


0338 


0796 


0847 


1305 


1356 


1814 


1865 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


53 


5.3 


10.6 


15.9 


21.2 


26.5 


31.8 


37.1 


42.4 


47.7 


52 


5.2 


10.4 


15.6 


20.8 


26.0 


31.2 


36.4 


41.6 


46.8 


51 


5.1 


10.2 


15.3 


20.4 


25.5 


30.6 


35.7 


40.8 


45.9 


50 


5.0 


1 10.0 


1 15.0 


20.0 


25.0 


30.0 


35.0 


40.0 


45.0 



LOGARITHMS OF NUMBERS. 



457 



No. 


855 L. 931.] 




[No. 899 L. 954. 


N. 





1 


2 


3 


4 


6 


6 


7 


8 


9 


Diff. 


855 


931966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 




6 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 




7 


2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 




8 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 




9 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 




860 


4498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 




1 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 




2 


5507 


5558 


5608 


5658 


5709 


5759 


5809 


5860 


5910 


5960 




3 


6011 


6061 


6111 


6162 


6212 


6262 


6313 


6363 


6413 


6463 




4 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 




5 


7016 


7066 


7116 


7167 


7217 


7267 


7317 


7367 


7418 


7468 




6 


7518 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 


50 


7 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


8 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 




9 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 




870 


9519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 




1 


940018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


Oi67 


2 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 




3 


1014 


1064 


1114 


1163 


1213 


1263 


1313 


1362 


1412 


1462 




4 


15il 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 




5 


2008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 




6 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 




7 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 




8 


3495 


3544 


3593 


3643 


3692 


3742 


3791 


3841 


3890 


3939 




9 


3989 


4038 


4088 


4137 


4186 


4236 


4285 


4335 


4384 


4433 




880 


4483 


4532 


4581 


4631 


4680 


4729 


4779 


4828 


4877 


4927 




1 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419 




2 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 




3 


6961 


6010 


6059 


6108 


6157 


6207 


6256 


6305 


6354 


6403 




4 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 




5 


6943 


6992 


7041 


7090 


7139 


7189 


7238 


7287 


7336 


7385 


49 


6 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 


7 


7924 


7973 . 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 




8 


8413 


8462 


8511 


8560 


8608 


8657 


8706 


8755 


8804 


8853 




9 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 




890 


9390 


9439 


9488 


9536 


9585 


9634 


9683 


9731 


9780 


9829 




1 


9878 


9926 


9975 


















0024 
0511 


0073 
0560 


0121 
0608 


0170 
0657 


0219 
0706 


0267 
0754 


0316 
0803 




2 


950365 


0414 


0462 




3 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289 




4 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


1775 




5 


1823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 




6 


2308. 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 




7 


2792 


2841 


2889 


2938 


2986 


3034 


3083 


3131 


3180 


3228 




8 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


3711 




9 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 


























, 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


51 
50 
49 

48 


5.1 
5.0 
4.9 

4.8 


10.2 
10.0 
9.8 
9.6 


15.3 
15.0 
14.7 
14.4 


20.4 
20.0 
19.6 
19.2 


25.5 
25.0 
24.5 
24.0 


30.6 
30.0 
29.4 

28.8 


35.7 

m.o 

34.3 
33.6 


40.8 
40.0 
39.2 
38.4 


45.9 
45.0 
44.1 
43.2 



458 



LOGARITHMS OF NUMBERS. 



No 


900 L. 954.1 














[N 


o. 944 L. 975. 


N. 





1 


2 


3 


4 


5 


« 


7 


8 


9 


Diff. 


900 


954243 


4291 


4339 


4387 


4435 


4484 


4532 


4580 


4628 


4677 




1 


4725 


4773 


4821 


4869 


4918 


4966 


5014 


5062 


5110 


5158 




2 


5207 


5255 


5303 


5351 


5399 


5447 


5495 


5543 


5592 


5640 




3 


5688 


5736 


5784 


5832 


5880 


5928 


5976 


6024 


6072 


6120 




4 


6168 


6216 


6265 


6313 


6361 


6409 


6457 


6505 


6553 


6601 


43 


5 


6649 


6697 


6745 


6793 


6840 


6888 


6936 


6984 


7032 


7080 


6 


7128 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


7512 


7559 




7 


7607 


7655 


7703 


7751 


7799 


7847 


7894 


7942 


7990 


8038 




8 


8086 


8134 


8181 


8229 


8277 


8325 


8373 


8421 


8468 


8516 




9 


8564 


8612 


8659 


8707 


8755 


8803 


8850 


8898 


8946 


8994 




910 


9041 


9089 


9137 


9185 


9232 


9280 


9328 


9375 


9423 


9471 




1 


9518 


9566 


9614 


9661 


9709 


9757 


9804 


9852 


9900 


9947 




2 


9995 






















0042 


0090 


0138 


0185 


0233 


0280 


0328 


0876 


0423 




3 


960471 


0518 


0566 


0613 


0661 


0709 


0756 


0804 


0851 


0899 




4 


0946 


0994 


1041 


1089 


1136 


1184 


1231 


1279 


1326 


1374 




5 


1421 


1469 


1516 


1563 


1611 


1658 


1706 


1753 


1801 


1848 




6 


1895 


1943 


1990 


2038 


2085 


2132 


2180 


2227 


2275 


2322 




7 


2369 


2417 


^64 


2511 


2559 


2606 


2653 


2701 


2748 


2795 




8 


2843 


2890 


2937 


2985 


3032 


3079 


3126 


3174 


3221 


3268 




9 


3316 


3363 


3410 


3457 


3504 


3552 


3599 


3646 


3693 


3741 




920 


3788 


3835 


3882 


3929 


3977 


4024 


4071 


4118 


4165 


4212 




1 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


4637 


4684 




2 


4731 


4778 


4825 


4872 


4919 


4966 


5013 


5061 


5108 


5155 




3 


5202 


5249 


5296 


5343 


5390 


5437 


5484 


5531 


5578 


5625 




4 


5672 


5719 


5766 


5813 


5860 


5907 


5954 


6001 


6048 


6095 


47 


5 


6142 


6189 


6236 


6283 


6329 


6376 


6423 


6470 


6517 


6564 




6 


6611 


6658 


6705 


6752 


6799 


6845 


6892 


6939 


6986 


7033 




7 


7080 


7127 


7173 


7220 


7267 


7314 


7361 


7408 


7454 


7501 




8 


7548 


7595 


7642 


7688 


7735 


7782 


7829 


7875 


7922 


7969 




9 


8016 


8062 


8109 


8156 


8203 


8249 


8296 


8343 


8390 


8436 




930 


8483 


8530 


8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 




1 


8950 


8996 


9043 


9090 


9136 


9183 


9229 


9276 


9323 


9369 




2 


9416 


9463 


9509 


9556 


9602 


9649 


9695 


9742 


9789 


9835 




3 


9882 


9928 


9975 


















0021 
0486 


0068 


0114 


0161 


0207 


0254 


0300 




4 


970347 


0393 


0440 


0533 


0579 


0626 


0672 


0719 


0765 




5 


0812 


0858 


0904 


0951 


0997 


1044 


1090 


1137 


1183 


1229 




6 


1276 


1322 


1369 


1415 


1461 


1508 


1554 


1601 


1647 


1693 




7 


1740 


1786 


1832 


1879 


1925 


1971 


2018 


2064 


2110 


2157 




8 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 




9 


2666 


2712 


2758 


2804 


2851 


2897 


2943 


2989 


3035 


3082 




940 


3128 


3174 


3220 


3266 


3313 


3359 


3405 


3451 


3497 


3543 




1 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


3913 


3959 


4005 




2 


4051 


4097 


4143 


4189 


4235 


4281 


4327 


4374 


4420 


4466 




3 


4512 


4558 


4604 


4650 


4696 


4742 


4788 


4834 


4880 


4926 




4 


4972 


5018 


5064 


5110 


5156 


5202 


5248 


5294 


5340 


5386 


46 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


47 
46 


4.7 
4.6 


9.4 
9.2 


14.1 
13.8 


18.8 
18.4 


23.5 
23.0 


28.2 
27.6 


32.9 
32.2 


37.6 
36.8 


42.3 
41 4 



LOGARITHMS OF NUMBERS. 



459 



yio. 


m L. 975.] 














[No. 989 L. 995. 


N. 





1 


8 


3 


4 


5 

5662 


6 


7 


8 


9 


Diff. 


945 


975432 


5478 


5524 


5570 


5616 


5707 


5753 


5799 


6845 




6 


5891 


5937 


5983 


6029 


6075 


0121 


6167 


6212 


6258 


6304 




7 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 




8 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 




9 


7266 


7312 


7358 


7403 


7449 


7495 


7541 


7586 


7632 


7678 




950 


7724 


7769 


7815 


7861 


7906 


7952 


7998 


8043 


8089 


8135 




1 


8181 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 




2 


8637 


8683 


8728 


8774 


8819 


8865 


8911 


8956 


9002 


9047 




3 


9093 


9138 


9184 


9230 


9275 


9321 


9366 


9412 


9457 


9503 




4 


9548 


9594 


9639 


9685 


9730 


9776 


9821 


9867 


9912 


9958 




5 


980003 


0049 


0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 




6 


0458 


0503 


0549 


0594 


0640 


0685 


0730 


0776 


0821 


0867 




7 


0912 


0957 


1003 


1048 


1093 


1139 


1184 


1229 


1275 


1320 




8 


1366 


1411 


1456 


1501 


1547 


1592 


1637 


1683 


1728 


1773 




9 


1819 


1864 


1909 


1954 


2000 


2045 


2090 


2135 


2181 


2226 




960 


2271 


2316 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 




1 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 




2 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


3581 




3 


3626 


3671 


3716 


3762 


3807 


3852 


3897 


3942 


3987 


4032 




4 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


4482 


45 


5 


4527 


4572 


4617 


4662 


4707 


4752 


4797 


4842 


4887 


4932 


6 


4977 


5022 


5067 


5112 


5157 


5202 


5247 


5292 


5337 


5382 




7 


5426 


5471 


5516 


5561 


5606 


5651 


5696 


5741 


5786 


5830 




8 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


6279 




9 


6324 


6369 


6413 


6458 


6503 


6548 


6593 


6637 


6682 


6727 




970 


6772 


6817 


6861 


6906 


6951 


6996 


7040 


7085 


7130 


7175 




1 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 




2 


7666 


7711 


7756 


7800 


7845 


7890 


7934 


7979 


8024 


8068 




3 


8113 


8157 


8202 


8247 


8291 


8336 


8381 


8425 


8470 


8514 




4 


8559 


8604 


8648 


8693 


8737 


8782 


8826 


8871 


8916 


8960 




5 


9005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 




6 


9450 


9494 


9539 


9583 


9628 


9672 


9717 


9761 


9806 


9850 




7 


9895 


9939 


9983 


















0028 
0472 


0072 
0516 


0117 
0561 


0161 
0605 


0206 
0650 


0250 
0694 


0294 
0738 




8 


990339 


0383 


0428 




9 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


1137 


1182 




980 


1226 


1270 


1315 


1359 


1403 


1448 


1492 


1536 


1580 


1625 




1 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 




2 


2111 


2156 


2200 


2244 


2288 


23a3 


2377 


2421 


2465 


2509 




3 


2554 


2598 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 




4 


2995 


3039 


3083 


3127 


3172 


3216 


3260 


3304 


3348 


3392 




5 


3436 


3480 


3524 


3568 


3613 


3657 


3701 


3745 


3789 


3833 




6 


3877 


3921 


3965 


4009 


4053 


4097 


4141 


4185 


4229 


4273 




7 


4317 


4361 


4405 


4449 


4493 


4537 


4581 


4625 


4669 


4713 


44 


8 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5065 


5108 


5152 




9 


5196 


5240 


5284 


5328 


5372 


5416 


5460 


55U4 


5547 


5591 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


46 


4.6 


9.2 


13.8 


18.4 


23.0 


27.6 


32.2 


36.8 


45 


4.5 


9.0 


13.5 


18.0 


22 5 


27.0 


31.5 


36.0 


44 


4.4 


8.8 


13.2 


17.6 


22.0 


26.4 


30.8 


35.2 


43 


4.3 


8.6 


12.9 


17.2 


21.5 


25.8 


30.1 


34.4 



41.4 1 

40.5 1 

39.6 I 
38.71 



460 



L06AEITHMS OP NUMBERS. 



No. 


390 L. 995.] 














[N 


o. 999 L. 999. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


990 


995635 


5679 


5723 


5767 


5811 


5854 


5898 


5942 


5986 


6030 




1 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 


2 


6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 




8 


6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 




4 


7386 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 




5 


7823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 




6 


8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 




7 


8695 


8739 


8782 


8826 


8869 


8913 


8956 


9000 


9043 


9087 




8 


9131 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 




9 


9565 


9609 


9652 


9696 


9739 


9783 


9826 


9870 


9913 


9957 


43 



Constant Numbers and their Logarithms. 



Symbol. 


Number. 


Logarithm. 


TT 


3.141 592 653 590 


0.497 149 872 694 




27r 


6.283 185 307 180 


0.798 179 868 35S 




377 


9.424 777 960 769 


0.974 271 127 414 




47r 


12.566 370 614 359 


1.099 209 864 022 




577 


15.707 963 267 950 


1.196 119 877 080 




677 


18.849 555 921 539 


1.275 301 123 078 




777 


21.991 148 575 119 


1.34-2 247 912 708 




877 


25.132 741 228 718 


1.400 239 859 686 




977 


28.274 333 882 308 


1.451392 382 133 




;;T 


0.523 598 775 598 


T.718 998 622 310 




; :'"■ 


0.785 398 163 397 


T.895 089 881366 




; 77 


1.570 796 326 795 


0.196 119 877 030 




': 1^ 


4.187 790 204 786 


0.622 088 609 302 




172 


9.869 604 401089 


0.994 299 745 388 




773 


31.006 276 680 293 


1.491449 618 082 




Vn 


1.772 453 850 906 


0.248 574 936 347 




v^ 


1.464 591887 562 


0.165 716 624 231 




1/77 


0.318 309 886 184 


T.502 850 127 306 




180/77 


57.295 779 513 025 


1.758 122 632 409 




1/772 


0.101321 183 642 


T.005 700 254 612 




1/4/77 


0.564 189.583 548 


T.751425 063 653 




logg'T 


1.144 729 885 849 


0.058 703 021 240 




arcl** 


0.017 453 292 520 


■2.241877 367 591 




sin 1° 


0.017 452 406 417 


2". 241 855 318 418 




arc 1' 


0.000 290 888 209 


T.463 726 117 207 




sin 1' 


0.000 290 888 205 


T.463 726 111082 




arc 1" 


0.000 004 848 137 


■g-.685 574 866 824 




sin 1" 


0.000 004 848 137 


-6.685 574 866 822 




e 


2.718 281828 459 


0.434 294 481 903 




M 


0.434 294 481 903 


T.637 784 311301 




1/M 


2.302 585 092 994 


0.362 215 688 699 




V2 


1.414 213 562 373 


0.150 514 997 832 




V3 


1.732 050 807 569 


0.238 560 627 360 




V5 


2.236 007 977 477 


0.349 485 002 168 





TRIGONOMETRIC FORMULA. 



TRIG-ONOMETRIOAL FUNCTIONS. 

Right-angled Triangles. 

Let A (Fig. 1) = angle B AC = arc BF, and let the radius AF = AB = 
AH= 1. 



We then have 




* sin^ 


= BG 


cos^ 


= AG 


tan^ 


= DF 


cot A 


= HG 


sec A 


= AI> 


cosec A 


= AG 


versin A 


= CF= BE 


covers A 


= BK= HL 


exsec A 


= BD 


coexsec A 


- BG 


chord A 


= BF 


chord 2 A 


= BI= 2BG 



1 


I K 


G 




"> 


r^ 


L 




i 




1 

h 



Fig. 1. 



In the right-angled triangle ABC (Fig. 1) 
Let AB = c, AC = 6, and BC = a. 
We then have : 



1. sin A 

2. cos A 

3. tan A 

4. cot A 

5. sec A 



= — = cos B 
c 

=: — =: Sin B 
C 

a 
= rr — cot B 
b 

b 

=z — ~ tan B 
a 



= -r- =: cosec B 




6. cosec A = 



= sec B 



7, vers ^ 



c -b 

■ = covers B 



exsec A = — , — ■ = coexsec B 



10. coexsec A = = exsec B 

a 



11. a = c sin A ~ b tan A 

12. 6 = c cos ^ = a cot A 
a b 



13. c = 



21. area = 



sin A cos A 

14. a = c cos B ~b cot ^ 

15. b = c sin B — a tan 5 

16. C =: = . — ^ 

COS B sm ^ 

l*^- « = i^ (c H- 6) (c - 6) 

18. b = V(c'+-^(S~^Ila) 

19. c = Va2-|-62 

20. a = 90« = ^ + B 
a6 



461 



46S 



TRIGOl^OMETRICAL FU:N^CTI0NS. 







Plane Triang^les. 






V 

a/ 






Fig. 2. 




GIVEN. 


BOUGHT. 


FORMULA. 


22 


A,B,a 


a,6,c 


/^ 1ftno <' '1 1 7?^ ?) — '?iTi R 


O — lOU l.^ -\- 15)^ O ^^ ^ . Sin J3, 








/- ^ 'sin (A \ R\ 


"" ~ Sin ^ "''' ^^^ ' ^^ 


23 


A,a,h 


B, C, c 


sm^=:^^5_^.&, c= 180«-U+^X 
c ^ -in C 


sin ^ ' " 


24 


C,a,b 


^u + ^x 


1^ U + ^) = 90- - 3^ a 


25 




}4U'-B) 


tan J^ ( Jl - ^) = ^^ tan ^ U + 5) 


26 




A,B 


^ = ^ (4 + -5) - ^ U - 5) 


27 




c 




28 
29 

80 


a, &, e 


area 


^ = 3^ a 6 sin C. 


Let s = 3^(a+ 6 +c):sin^^ =\/^^^lv^^ 


^"* y he ^"^ y sis— a) 


81 






. , 2^s(s - a)(s-6)(s-c) 


sin^- ^^ 


32 




area 


6c 


£- = Vs{s-a) is- b) is - c) 


33 


A,B,C,a 


area 


a* sin 5 . sin C 
2 sin ^ 



Table 84 
SINES, COSINES. SECANTS, AND COSECANTS. 



"o 


0° 1 


1° 1 


2° I 


30 1 


40 


60 


Sine 


Cosin 


Sine 

.01745 


Cosin 

.99985 


Sine 
.03490 


Cosin 
.99939 


Sine 


Cosin 

799863 


Sine 


Cosin 


Tooooo 


One. 


.05234 


.06976 


.99756 


1 


.00029 


One. 


.01774 


.99984 


.03519 


.99938 


.05263 


.99861 


.07005 


.99754 


59 


2 


.00058 


One. 


.01803 


.99984 


.03548 


.99937 


.05292 


.99860 


.07034 


.99752 


58 


3 


.00087 


One. 


.01832 


.99983 


.03577 


.99936 


.05321 


.99858 


.07063 


.99750 


57 


4 


.00116 


One. 


.01862 


.99983 


.03606 


.99935 


.05350 


.99857 


.07092 


.99748 


56 


5 


.00145 


One. 


.01891 


.99982 


.03635 


.99934 


.05379 


.99855 


.07121 


.99746 


55 


6 


.00175 


One. 


.01920 


.99982 


.03664 


.99933 


.05408 


.99854 


.07150 


.99744 


54 


7 


.00204 


One. 


.01949 


.99981 


.03693 


.99932 


.05437 


.99852 


.07179 


.99742 


53 


8 


.00233 


One. 


.01978 


.99980 


.03723 


.99931 


.05466 


.99851 


.07208 


".99740 


52 


9 


.00262 


One. 


.02007 


.99980 


.03752 


.99930 


.05495 


.99849 


.07237 


.99738 


51 


10 


.00291 


One. 


.02036 


.99979 


.03781 


.99929 


.05524 


.99847 


.07266 


.99736 


60 


11 


.00320 


.99999 


.02065 


.99979 


.03810 


.99927 


.05553 


.99846 


.07295 


.99734 


49 


12 


.00349 


.99999 


.02094 


.99978 


.03839 


.99926 


.05582 


.99844 


.07324 


.99731 


48 


13 


.00378 


.99999 


.02123 


.99977 


.03868 


.99925 


.05611 


.99842 


.07353 


.99729 


47 


14 


.00407 


.99999 


.02152 


.99977 


.03897 


.99924 


.05640 


.99841 


.07382 


.99727 


46 


15 


.00436 


.99999 


.02181 


.99976 


.03926 


.99923 


.05669 


.99839 


.07411 


.99725 


45 


16 


.00465 


.99999 


.02211 


.99976 


.03955 


.99922 


.05698 


.99838 


.07440 


.99723 


44 


17 


.00495 


.99999 


.02240 


.99975 


.03984 


.99921 


.05727 


.99836 


.07469 


.99721 


43 


18 


.00524 


.99999 


.02269 


.99974 


.04013 


.99919 


.05756 


.99834 


.07498 


.99719 


42 


19 


.00553 


.99998 


.02298 


.99974 


.04042 


.99918 


.05785 


.99833 


.07527 


.99716 


41 


20 


.00582 


.99998 


.02327 


.99973 


.04071 


.99917 


.05814 


.99831 


.07556 


.99714 


40 


21 


.00611 


.99998 


.02356 


.99972 


.04100 


.99916 


.05S44 


.99829 


.07585 


.99712 


39 


22 


.00640 


.99998 


.02385 


.99972 


.04129 


.99915 


.05873 


.99827 


.07614 


.99710 


38 


23 


.00669 


.99998 


.02414 


.99971 


.04159 


.99913 


.05902 


.99826 


.(7643 


.99708 


37 


24 


.00698 


.99998 


.02443 


.99970 


.04188 


.99912 


.05931 


.99824 


.07672 


.99705 


36 


25 


.00727 


.99997 


.02472 


.99969 


.04217 


.90911 


.05960 


.99822 


.07701 


.99703 


35 


26 


.00756 


.99997 


.02501 


.99969 


.04246 


.99910 


.05989 


.99821 


.07730 


.99701 


34 


27 


.00785 


.99997 


.02530 


.99968 


.04275 


.99909 


.06018 


.99819 


.07759 


.99699 


33 


28 


.00814 


.99997 


.02560 


.99967 


.04304 


.99907 


.06047 


.99817 


.07788 


.99696 


32 


29 


.00844 


.99996 


.02589 


.99966 


.04333 


.99906 


.06076 


.99815 


.07817 


.99694 


31 


30 


.00873 


.99996 


.02618 


.99966 


.04362 


.99905 


.06105 


.99813 


.07846 


.99692 


30 


31 


.00902 


.99996 


.02647 


.99965 


.04391 


.99904 


.06134 


.99812 


.07875 


.99689 


29 


32 


.00931 


.99996 


.02676 


.99964 


.04420 


.99902 


.06163 


.99810 


.07904 


.99687 


28 


33 


.00960 


.99995 


.02705 


.99963 


.04449 


.99901 


.06192 


.99808 


.07933 


.99685 


27 


34 


.00989 


.99995 


.02734 


.99963 


.04478 


.99900 


.06221 


.99806 


.07962 


.99683 


26 


35 


.01018 


.99995 


.02763 


.99962 


.04507 


.99898 


.06250 


.99804 


.07991 


.99680 


25 


36 


.01047 


.99995 


.02792 


.99961 


.04536 


.99897 


.06279 


.99803 


.08020 


.99678 


24 


37 


.01076 


.99994 


.02821 


.99960 


.04565 


.99896 


.06308 


.99801 


.08049 


.99676 


23 


38 


.01105 


.99994 


.02850 


.99959 


.04594 


.99894 


.06337 


.99799 


.08078 


.99673 


22 


39 


.01134 


.99994 


.02879 


.99959 


.04623 


.99893 


.06366 


.99797 


.08107 


.99671 


21 


40 


.01164 


.99993 


.02908 


.99958 


.04653 


.99892 


.06395 


.99795 


.08136 


.99668 


20 


41 


.01193 


.99993 


.02938 


.99957 


.04682 


.99890 


.06424 


.99793 


.08165 


.99666 


19 


42 


.01222 


.99993 


.02967 


.99956 


.04711 


.99889 


.06453 


.99792 


.08194 


.99664 


18 


43 


.01251 


.99992 


.02996 


.99955 


.04740 


.99888 


.06482 


.99790 


.08223 


.99661 


17 


44 


.01280 


.99992 


.03025 


.99954 


.04769 


.99886 


.06511 


.99788 


.08252 


.99659 


16 


45 


.01309 


.99991 


.03054 


.99953 


.04798 


.99885 


.06540 


.99786 


.08281 


.99657 


15 


46 


.01338 


.99991 


.03083 


.99952 


.04827 


.99883 


.06569 


.99784 


.08310 


.99654 


14 


47 


.01367 


.99991 


.03112 


.99952 


.04856 


.99882 


.06598 


.99782 


.08339 


.99652 


13 


48 


.01396 


.99990 


.03141 


.99951 


.04885 


.99881 


.06627 


.99780 


.08368 


.99649 


12 


49 


.01425 


.99990 


.03170 


.99950 


.04914 


.99879 


.06656 


.99778 


.08397 


.99647 


11 


60 


.01454 


.99989 


.03199 


.99949 


.04943 


.99878 


.06685 


.99776 


.08426 


.99644 


10 


51 


.01483 


.99989 


.03228 


.99948 


.04972 


.99876 


.06714 


.99774 


.08455 


.99642 


9 


52 


.01513 


.99989 


.03257 


.99947 


.05001 


.99875 


.00743 


.99772 


.08484 


.99639 


8 


53 


.01542 


.99988 


.03286 


.99946 


.05030 


.99873 


.06773 


.99770 


.08513 


.99637 


7 


54 


.01571 


.99988 


.03316 


.99945 


.05059 


.99872 


.06802 


.99768 


.08542 


.99635 


6 


.'35 


.01600 


.99987 


.03345 


.99944 


.05088 


.99870 


.06831 


.99766 


.08571 


.99632 


5 


56 


.01629 


.99987 


.03374 


.99943 


.05117 


.99869 


.06860 


.99764! 


.08600 


.99630 


4 


57 


.01658 


,99986 


.03403 


.99942 


.05146 


.99867 


.06889 


.99762' 


.08629 


.99627 


3 


r8 


.01687 


.99986 


.03432 


.99941 


.05175 


.99866 


.06918 


.99760! 


.08658 


.99625 


2 


59 


.01716 


.99985 


.03461 


.99940 


.05205 


.99864 


.06947 


.99758! 


.08687 


.99622 


1 


GO 
/ 


.01745 
Cosin 


.99985 
Sine 


.03490 
Cosin 


.99939 
Sine 


.05234 


.99803 


.0Q976 
Cosin 


.99756 
Sine 


.08716 
Cosin 


.99619 
Sine 


J) 


Cosin 


Sine 


89° 1 


88° 1 


87° 1 


86° 1 


85° 


' 










4 


m 













464 



SINES AND COSINES. 





5° I 


6° 1 


70 1 


8« 1 


9° 1 


/ 




Sine 


Cosin 1 


Sine 


Cosin ! 


Sine ! 


Cosin ' 


Sine 


Cosin 


Sine 


Cosin 





.08716 


.99619s 


.10453 


.99452 


.121871 


.99255 


^13917 


.9902i' 


.15643 


.98769 


60 


1 


.08745 


.99617 


.10482 


.99449 


.122161 


.99251 


.13946 


.99023 


.15672 


.98764 


59 


2 


.08774 


.99614 


.10511 


.99446 


.122451 


.99248 


.13975 


.99019 


.15701 


.98760 


58 


3 


.08803 


.996121 


.10540 


.99443 


.12274, 


.99244 


.14004 


.99015 


.15730 


.98755 


57 


4 


.08831 


.99609 


.10569 


.99440 


.12302 


.99240 


.14033 


.99011 


.15758 


.98751 


55 


5 


.08860 


.99607 


.10597 


.99437 


.123311 


.99237; 


.14061 


.99006 


.15787 


.98746 


55 


6 


.08889 


.996041 


.10626 


.99434 


.12360 


.99233 


.14090 


.99002 


.15816 


.98741 


54 


7 


.08918 


.99602 


.10655 


.99431 


.12389 


. 99230 1 


.14119 


.98998 


.15845 


.98737 


53 


8 


.08947 


.99599 


.10684 


.99428 


.124181 


.99226 


.14148 


.98994 


.15873 


.98732 


52 


9 


.08976 


.99596 


.10713 


.99424 


.124471 


.99222 


.14177 


.98990 


.15902 


.98728 


51 


io 


.09005 


.99594 


.10742 


.99421; 


.12476 


. 99219 ^ 


.14205 


.98986 


.15931 


.98723 


50 


il 


.09034 


.99591 


.10771 


.994181 


.12504 


.99215' 


.14234 


.98982 


.15959 


.98718 


49 


12 


.09063^ 


.99588 


.10800 


.99415' 


.12533; 


.99211 


.14263 


.98978 


.15988 


.98714 


48 


13 


.09092 


.99586 


.10829' 


.99412: 


.12562 


.99208 


.14292 


.98973 


1.16017 


.98709 


47 


14 


.09121 


.99583 


.10858 


.99409 


.12591 


.99204 


.14320 


.98969 


.16046 


.98704 


46 


15 


.09150 


.99580 


.10887 


.99406 


.12620 


.992001 


.14349 


.98965 


.16074 


.98700 


45 


16 


.09179 


.99578 


.10916 


.99402, 


.12349 


.991971 


.14378 


.98961 


.16103 


.98695 


44 


17 


.09208 


.99575 


.10945 


.99399 


.126781 


.99193^ 


.14407 


.98957 


; .16132 


.98690 


43 


18 


.09237 


.99572 


.10973 


.99396' 


.127061 


.991891 


.14436 


.98953 


i .16160 


.98686 


42 


19 


.09266 


.99570 


.11002 


.99393 


.12735 


.99186; 


.14464 


.98948 


.16189 


.98681 


41 


20 


.09295 


.99567 


.11031 


.99390: 


.12764 


.99182 


.14493 


.98944 


.16218 


.98676 


40 


21 


.09324 


.99564 


.11060 


.993861- 


.12793 


.99178 ! 


.14522 


.98940 


.16246 


.98671 


39 


22 


.09353 


.99562 


.11039 


.993831 


.12822 


.99175, 


.14551 


.98936 


.16275 


.98667 


38 


23 


.09382 


.99559 


.11118 


.99380 


.12851 


.991711 


.14580 


.98931 


'.16304 


.98662 


37 


24 


.09411 


.99556 


.11147 


.99377 


.12880 


.991671 


.14608 


.98927 


.16333 


.98657 


36 


25 


.09440 


.99553 


.11176 


.99374 


.12908 


.99163 


.14637 


.98923 


.16361 


.98652 


35 


26 


.09469 


.99551 


.11205 


.99370 


.12937 


.99160 


.14666 


.98919 


.16390 


.98648 


34 


27 


.09498 


.99548 


.11234 


.99367 


.12966 


.99156 


.14695 


.98914 


1.16419 


.98643 


33 


28 


.09527 


.99545 


.11263 


.99864 


.12995 


.99152 


.14723 


.98910 


'.16447 


.98638 


32 


29 


.09556 


.99542 


.11291 


.99360 


.13024 


.99148 


.14752 


.98906 


1.16476 


.98633 


31 


30 


.09585 


.99540 


1 .11320 


.99357 


.13053 


.99144 


.14781 


.98902 


.16505 


.98629 


30 


31 


.09614 


.99537 


.11349 


.99354' 


.13081 


.99141 


.14810 


.98897 


.16533 


.98624 


29 


32 


.09642 


.99534 


.11378 


.99351 


.13110 


.99137 


.14838 


.98893 


.16562 


.98619 


28 


33 


.09671 


.99531 


.11407 


.99347 


.13139 


.99133 


.14867 


.98889 


i .16591 


.98614 


27 


34 


.09700 


.99528 


.11436 


.99344 


.13168 


.99129 


.14896 


.98884 


.16620 


.98609 


26 


35 


.09729 


.99526 


.11465 


.99341 


.13197 


.99125 


.14925 


.98880 


1.16648 


.98604 


25 


36 


.09758 


.99523 


.11494 


.99337 


.13226 


.99122 


.14954 


.98876 


.16677 


.98600 


24 


37 


.09787 


.99520 


.11523 


.99334 


.13254 


.99118 


.14982 


.98871 


1 .16706 


.98595 


23 


38 


.09816 


.99517 


.11552 


.99331 


.13283 


.99114 


.15011 


.98867 


.16734 


.98590 


22 


39 


.09845 


.99514 


.11580 


.99327 


.13312 


.99110 


.15040 


.98863 


.16763 


.98585 


21 


40 


.09874 


.99511 


.11609 


.99324 


.13341 


.99106 


.15069 


.98858 


.16792 


.98580 


20 


41 


.09903 


.99508 


.11638 


.99320 


.13370 


.99102 


.15097 


.98854 


.16820 


.98575 


19 


42 


.09932 


.99506 


.11667 


.99317 


.13399 


.99098 


.15126 


.98849 


.16849 


.98570 


18 


43 


.09961 


.99503 


.11696 


.99314 


.13427 


.99094 


.15155 


.98845 


L 16878 


.98565 


17 


44 


.09990 


.99500 


.11725 


.99310 


.13456 


.99091 


.15184 


.98841 


.16906 


.98561 


16 


45 


.10019 


.99497 


.11754 


•99307 


.13485 


.99087 


.15212 


.98836 


1.16935 


.98556 


15 


46 


.10048 


.99494 


.11783 


.99303 


.13514 


.99083 


.15241 


.98832 


' .16964 


.98551 


14 


47 


.10077 


.99491 


.11812 


.99300 


.13543 


.99079 


.15270 


.98827 


.16992 


.98546 


13 


48 


.10106 


.99488 


.11840 


.99297, 


.13572 


.99075 


.15299 


.98823 


1.17021 


.98541 


12 


49 


.10135 


.99485 


.11869 


.992931 


.13600 


.99071 


.15327 


.98818 


1 .17050 


.98536 


11 


50 


.10164 


.99482 


.11898 


.99290 


.13629 


.99067 


.15356 


.98814 


.17078 


.98531 


10 


51 


.10192 


.99479 


.11927 


.99286 


.13658 


.99063 


.15385 


.98809 


.17107 


.98526 


9 


52 


.10221 


.99476 


.11956 


.99283 


.13687 


.99059 


.15414 


.98805 


.17136 


.98521 


8 


53 


.10250 


.99473 


.11985 


.99279 


.13716 


.99055 


.15442 


.98800 


.17164 


.98516 


7 


54 


.10279 


.99470 


1.12014 


.99276 


.13744 


.99051 


.15471 


.98796 


.17193 


.98511 


6 


55 


.10308 


.99467 


' . 12043 


.99272 


.13773 


.99047 


.15500 


.98791 


.17222 


.98506 


5 


56 


.10337 


.99464 


1 . 12071 


.99269 


.13802 


.99043 


.15529 


.98787 


.17250 


.98501 


4 


57 


10366 


.99401 


.12100 


.99265 


.13831 


.99039 


.15557 


.98782 


.17279 


.98496 


3 


58 


.10395 


.99458 


.12129 


.99262 


.13860 


.99035 


.15586 


.98778 


1 .17308 


.98491 


2 


59 


.10424 


.99455 


.12158 


1.99258 


.13889 


.99031 


.15615 


.98773 


: .17336 


,.98486 


1 


60 


.10453 


.99452 


.12187 


i. 99255 


.13917 


.99027 


.15643 


.98769 


i .17365 


.98481 


_0 


/ 


Cosin 


Sine 


Cosin 


1 Sine 


Cosin 


Sine" 


Cosin 


Sine 


Cosin 


Sine 


/ 


84' 


83<» 


82» 


sv 


80° 



SIKES AND COSINES. 



465 



> 
-0 


10° 


11° 


12° 


13° 


14° 


/ 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 

.22495 


Cosin 


Sine 


Cosin 


.17365 


.98481 


.19081 


.98163 


.20791 


.97815 


.97437 


.24192 


.97030 


60 


1 


.17393 


.98476 


.19109 


.98157 


.20820 


.97809 


.22523 


.97430 


.24220 


.97023 


59 


2 


.17422 


.98471 


.19138 


.98152 


.20848 


.97803 


.22552 


.97424 


.24249 


.97015 


58 


3 


.17451 


.98466 


.19167 


.98146 


.20877 


.97797 


.22580 


.97417 


.24277 


.97008 


57 


4 


.17479 


.98461 


.19195 


.98140 


.20905 


.97791 


.22608 


.97411 


,24305 


.97001 


56 


5 


.17508 


.98455 


.19224 


.98135 


.20933 


.97784 


.22637 


.97404 


.24333 


.96994 


55 


6 


.17537 


.98450 


.19252 


.98129 


.20962 


.97778 


.22665 


-07398 


.24362 


.96987 


54 


7 


.17565 


.98445 


.19281 


.98124 


.20990 


.97772 


.22693 


.97391 


.24390 


.96980 


53 


8 


.17594 


.98440 


.19309 


.98118 


.21019 


.97766 


.22722 


.97384 


.24418 


.96973 


52 


9 


.17623 


.98435 


.19338 


.98112 


.21047 


.97760 


.22750 


.97378 


.24446 


.96966 


51 


10 


.17651 


.98430 


.19366 


.98107 


.21076 


.97754 


.22778 


.97371 


.24474 


.96959 


50 


11 


.17680 


.98425 


.19395 


.98101 


.21104 


.97748 


.22807 


.97365 


.24503 


.96952 


40 


12 


.17708 


.98420 


.19423 


.98096 


.21132 


.97742 


.22835 


.97358 


.24531 


.96945 


48 


13 


.17737 


.98414 


.19452 


.98090 


.21161 


.97735 


.22863 


.97351 


.24559 


.96937 


47 


14 


.17766 


.98409 


.19481 


.98084 


.21189 


.97729 


.22892 


.97345 


.24587 


.96930 


46 


15 


.17794 


.98404 


.19509 


.98079 


.21218 


.97723 


.22920 


.97338 


.24615 


.96923 


45 


16 


.17823 


.98399 


.19538 


.98073 


.21246 


.97717 


.22948 


.97331 


.24644 


.96916 


44 


17 


.17852 


.98394 


.19566 


.98067 


.21275 


.97711 


.22977 


.97325 


.24672 


.96909 


43 


18 


.17880 


.98389 


.19595 


.98061 


.21303 


.97705 


.23005 


.97318 


.24700 


.96902 


42 


19 


.17909 


.98383 


.19623 


.98056 


.21331 


.97698, 


.23033 


.97311 


.24728 


.96894 


41 


20 


.17937 


.98378 


.19652 


.98050 


.21360 


.97692 


.23062 


.97304 


.24753 


.96887 


40 


21 


.17966 


.98373 


.19680 


.98044 


.21388 


.97686 


.23090 


.97298 


.24784 


.96880 


39 


22 


.17995 


.98368 


.19709 


.98039 


.21417 


.976801 


.23118 


.972911 


.24813 


.96873 


38 


23 


.18023 


.98362 


.19737 


.98033 


.21445 


.976731 


.23146 


.972841 


.24841 


.96866 


37 


24 


.18052 


.98357 


.19766 


.98027 


.21474 


.97667 


.23175 


.97278 


.24869 


.96858 


36 


25 


.18081 


.98352 


.19794 


.98021 


.21502 


.97661 


.23203 


.97271 


.24897 


.96851 


35 


26 


.18109 


.98347 


.19823 


.98016 


.21530 


.97655 


.23231 


.97264 


.24925 


.96844 


34 


27 


.18138 


.98341 


.19851 


.98010 


.21559 


.97648 


.23260 


.97257 


.24954 


.96837 


33 


28 


.18166 


.98336 


.19880 


.98004 


.21587 


.97642 


.23288 


.97251 


.24982 


.96829 


32 


29 


.18195 


.98331 


.19908 


.97998 


.21616 


.97636 


.23316 


.97244 


.25010 


.96822 


31 


30 


.18224 


.98325 


.19937 


.97992 


.21644 


.97630 


.23345 


.97237 


.25038 


.96815 


30 ] 


31 


.18252 


.98320 


.19965 


.97987 


.21672 


.97623 


.23373 


.97230 


.25066 


.96807 


29 


32 


.18281 


.98315 


.19994 


.97981 


.21701 


.97617 


.23401 


.97223 


.25094 


.96800 


28 


33 


.18309 


.98310 


.20022 


.97975 


.21729 


.97611 


.23429 


.97217 


.25122 


.96793 


27 


34 


.18338 


.98304 


.20051 


.97969 


.21758 


.97604 


.23458 


.97210 


.25151 


.96786 


26 


35 


.18367 


.98299 


.20079 


.97963 


.21786 


.97598 


.23486 


.97203 


.25179 


.96778 


25 


36 


.18395 


.98294 


.20108 


.97958 


.21814 


.97592 


.23514 


.97196 


.25207 


.96771 


24 


37 


.18424 


.98288 


.'^0136 


.97952 


.21843 


.97585 


.23542 


.97189 


.25235 


.96764 


23 


38 


.18452 


.98283 


.20165 


.97946 


.21871 


.97579 


.23571 


.97182 


.25263 


.96756 


22 


39 


.18481 


.98277 


.20193 


.97940 


.21899 


.97573 


.23599 


.97176 


.25291 


.96749 


21 


40 


.18509 


.98272 


.20222 


.97934 


.21928 


.97566 


.23627 


.97169 


.25320 


.96742 


20 


41 


.18538 


.98267 


.20250 


.97928 


.21956 


.97560 


.23656 


.97162 


.25348 


.96734 


19 


42 


.18567 


.98261 


.20279 


.97922 


.21985 


.97553 


.23684 


.97155 


.25376 


.96727 


18 


43 


.18595 


.98256 


.20307 


.97916 


.22013 


.97547 


.23712 


.97148 


.25404 


.96719 


17 


44 


.18624 


.98250 


.20336 


.97910 


.22041 


.97541 


.23740 


.97141 


.25432 


.96712 


16 


45 


.18652 


.98245 


.20364 


.97905 


.22070 


.97534 


.23769 


.97134 


.25460 


.96705 


15 


46 


.18681 


.98240 


.20393 


.97899 


.22098 


.97528 


.23797 


.97127 


.25488 


.96697 


14 


47 


.18710 


.98234 


.20421 


.97893 


.22126 


.97521 


.23825 


.97120 


.25516 


.96690 


13 


48 


.18738 


.98229 


.20450 


.97887 


.22155 


.97515 


.23853 


.97113 


.25545 


.96682 


12 


49 


.18767 


.98223 


.20478 


.97881 


.22183 


.97508 


.23882 


.97106 


.25573 


.96675 


11 


50 


.18795 


.98218 


.20507 


.97875 


.22212 


.97502 


.23910 


.97100 


.25601 


.96667 


10 


51 


.18824 


.98212 


.20535 


.97869 


.22240 


.97496 


.23938 


.97093 


.25629 


.96660 


9 


52 


.18852 


.98207 


.20563 


.97863 


.22268 


.97489 


.23966 


.970861 


.25657 .96653 


8 


53 


.18881 


.98201 


.20592 


.97857 


.22297 


.97483 


.2a995 


.97079 


.25685 .96645 


7 


54 


.18910 


.98196 


.20620 


.97851 


.22325 


.97476 


.24023 


.970721 


.25713 .96638 


6 


55 


.18938 


.98190 


.20649 


.97845 


.22353 


.97470 


.24051 


.97065; 


.25741 .96630 


5 


56 


.18967 


.98185 


.20677 


.97839 


.22382 


.97463 


.24079 


.97058 


.25769 .96623 


4 


57 


.18995 


.98179 


.20706 


.97833 


.22410 


.97457 


.24108 


.970511 


.25798 .96615 


3 


58 


.19024 


.98174 


.20734 


.97827 


.22438 


.97450 


.24136 


.97044 


.25826 .96608 


2 


59 


.19052 


.98168 


.20763 


.97821 


.22467 


.97444 


.24164 


.97037 


.25854 .96t)0O 


1 


60 

/ 


.19081 


.98163 


.20791 


.97815 


.22495 


.97437 


.24192 
Cosin 


.97030 
Sine 


.25882 .96593 
Cosin "Sine" 





Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 


79° 1 


78° ' 


77° 


1 76° 1 


76° 



466 



StNfiS AND COSINES. 






15° 


16° 1 


! 17° 1 


1 18° 


19° 


/ 

60 


Sine Cosin 

.25882 .96593 


Sine 
.27564 


Cosin 
.96126 


j Sine 


Cosin ' 


Sine 


Cosin 


Sine 
.32557 


Cosin 


' .29237 


.95630 


.30902 


.95106 


.94552 


1 


.25910 .96585 


.27592 


.96118 


.29265 


.95622. 


.30929 


.95CD7 


. 325^4 


.94542 


59 


2 


.25938 .96578 


.27620 


.96110 


.29293 


.95613 


.30957 


.95088 


.32612 


.94533 


58 


3 


.25966 .96570 


.27648 


.96102 


; .29321 


.95605 


.30985 


.95079 


.32639 


.94523 


57 


4 


.25994 .96562 


.27676 


.96094 


.29348 


.95596 


.31012 


.95070 


.32667 


.94514 


56 


5 


.26022 .96555 


.27704 


.96086 


.29376 


.95588 


.31040 


.95061 


.32694 


.94504 


55 


6 


.26050 .96547 


.27731 


.96078 


.29404 


.95579 


.31068 


.95052 


.32722 


.94495 


54 


7 


.26079 .96540 


.27759 


•96070 


.29432 


.955711 


.31095 


.95043 


.32749 


.94485 


53 


8 


.26107 .96532 


.27787 


.96062 


.29460 


.95562 


.31123 


.95033 


.32777 


.94476 


52 


9 


.26135 .96524 


.27815 


.90054 


.29487 


.95554 


.31151 


.95024 


.32804 


.94466 


51 


10 


.26163 .96517 


.27843 


.96046 


; .29515 


.95545 


; .31178 


.95015 


1 .32832 


.94457 


50 


11 


.26191 .96509* 


.27871 


.96037 


! .29543 


.95536 


1 .31206 


.95006 


.32859 


.94447 


49 


12 


.26219 .96502 


.27899 


.96029 


.29571 


.95528 


.31233 


.94997 


.32887 


.94438 


48 


13 


.26247!. 96494 


.27927 


.96021 


! .29599 


.95519 


.31261 


.94988 


.32914 


.94428 


47 


14 


.262751.96486 


.27955 


.96013 


, .29626 


.95511 


.31289 


.94979 


.32942 


.94418 


46 


15 


.263031.96479 


.27983 


.96005 


1 .29654 


.95502 


.31316 


.94970 


' .32969 


.94409 


45 


16 


.263311.96471 


.28011 


.95997 


, .29682 


.95493 


.31344 


.94961 


.32997 


.94399 


44 


17 


.26359 .96463 


.28039 


.95989 


.29710 


.95485 


.31372 


.94952 


.33024 


.94390 


43 


18 


.26387 .96456 


.28067 


.95981 


1 .29737 


.95476 


.31399 


.94943 


.33051 


.94380 


42 


19 


.26415 .96448 


.28095 


.95972 


1 .29765 


.95467 


.31427 


.94933 


! .33079 


.94370 


41 


20 


.26443 .96440 


.28123 


.95964 


j .29793 


.95459 


j .31454 


.94924 


1 .33106 


.94361 


40 


21 


.26471 .96433' 


.28150 


.95956 


! .29821 


.95450 


.31482 


.94915 


.33134 


.94351 


39 


22 


.265001.96425 


.28178 


.95948 


1 .29849 


.95441 


1 .31510 


.94906 


^ .33161 


.94342 


38 


23 


.26528^.96417 


.28206 


.95940 


.29876 


.95433 


! .31537 


.94897 


.33189 


.94332 


37 


24 


.26556;. 96410 


.28234 


.95931 


1 .29904 


.95424 


: .31565 


.94888 


.33216 


.94322 


36 


25 


.26584 


.96402 


.28262 


.95923 


' .29932 


.95415 


.31593 


.94878 


.33244 


.94313 


35 


26 


.26612 


.96394 


.28290 


.95915 


.29960 


.95407 


.31620 


.94869 


.33271 


.94303 


34 


27 


.26640 


.96386 


.28318 


.95907 


.29987 


.95398 


.31648 


.94860 


.33298 


.94293 


33 


28 


.26668 


.96379 


.28346 


.95898 


.30015 


.95389 


.31075 


.94851 


j .33326 


.94284 


32 


29 


.26696 


.96371 


.28374 


.95890 


.30043 


.95380 


.31703 


.94842 


1.33353 


.94274 


31 


30 


.26724 


. 96363 j 


.28402 


.95882 


.30071 


.95372 


j .31730 


.94832 


.33381 


.94264 


30 


31 


.26752 


.96355: 


.28429 


.95874 


.30098 


.95363 


' .31758 


.94823 


'.33408 


.94254 


29 


32 


.26780 


.96347 


.28457 


.95865 


.30126 


.95354 


1 .31786 


.94814 


.33436 


.94245 


28 


33 


.26808 


.96340 


.28485 


.95857 


.30154 


.95345 


' .31813 


.94805 


■ -33463 


.94235 


27 


34 


.26836 


.96332^ 


.28513 


.95849 


.30182 


.95337 


I .31841 


.94795 


1.33490 


.94225 


26 


35 


.26864 


.96324! 


.28541 


.95841 


.30209 


.95328 


.31868 


.94786 


! .33518 


.94215 


25 


36 


.26892 


.96316 


.28569 


.95832 


1 .30237 


.95319 


1 .31896 


.94777 


.33545 


.94206 


24 


37 


.26920 


.96308 


.28597 


.95824 


.30205 


.95310 


.31923 


.94768 


.33573 


.94196 


23 


38 


.26948 


.96301 


.28625 


.95816 


.30292 


.95301 


! .31951 


.94758 


.33600 


.94186 


22 


39 


.26976 


.96293 


.28652 


.95807 


.30320 


.95293 


! .31979 


.94749 


.33627 


.94176 


21 


40 


.27004 


.96285 


.28680 


.95799 


.30348 


.95284 


i .32006 


.94740 


i. 33655 


.94167 


20 


41 


.27032 


.96277' 


.28708 


.95791 


.30376 


.95275 


.32034 


.94730 


' .33682 


.94157 


19 


42 


.27060 


.96269; 


.28736 


.95782 


.30403 


.95260 


i .32061 


.94721 


.33710 


.94147 


IS 


43 


.27088 


.96261 


.28764 


.95774 


.30431 


.95257 


.32089 


.94712 


.33737 


.94137 


17 


44 


.27116 


.96253 


.28792 


.95766 


.30459 


.95248 


i .32116 


.94702 


.33764 


.94127 


16 


45 


.27144 


.96246 




.95757 


.30486 


.95240 


.32144 


.94693 


.33792 


.94118 


15 


46 


.27172 


.96238 


28847 


.95749 


i .30514 


.95231 


.32171 


.94684 


1 .33819 


.94108 


14 


47 


.27200 


.96230 


128875 


.95740 


1 .30542 


.95222 


.32199 


.94674 


.33846 


.94098 


13 


48 


.27228 


.96222 


.28903 


.95732 


1 .30570 


.95213 


.32227 


.94665 


.33874 


.94088 


12 


49 


.27256 


.96214 


.28931 


.95724 


! .30597 


.95204: 


.32254 


.94656 


i 33901 


.94078 


11 


60 


.272&4 


.96206, 


.28959 


.95715 


: .30625 


.95195, 


.32282 


.94646 


,.33929 


.94068 


10 


51 


.27312 


.96198 


.28987 


.95707 


.30653 


.951861 


.32309 


.94637 


1.33956 


.94058 


9 


52 


.27340 


.96190 


.29015 


.95698 


.30680 


.95177 


.32337 


.94627 


.33983 


.94049 


8 


53 


.27368 


.96182 


.29042 


.95690 


.30708 


.95168 


.32364 


.94618 


.34011 


.94039 


7 


54 


.27396 


.96174 


.29070 


.95681 


.30736 


.95159 


.32392 


.94609 


.34038 


.94029 


6 


55 


.27424;. 96166 


.29098 


.95673 


.30763 


.95150 


.32419 


.94599 


.34065 


.94019 


5 


56 


.27452 .96158 


.29126 


.95664 


.30791 


.95142 


.32447 


.94590 


.34093 


.94009 


4 


57 


.274801.96150 


.291.54 


.95656 


.30819 


.95133 


.32474 


.93580 


.34120 


.93999 


3 


58 


.27508 .96142 


.29182 


.95&47 


.30846 


.95124 


.32502 


.94571 


.34147 


.93989 


2 


59 


.27536 .96134 


.29209 


.95639 


.30874 


.95115 


.32529 


.94561 


.34175 


.93979 


1 


60 


.275641.96126 
Cosin Sine | 


.29237 


.95630 


.30902 
Cosin 


.95106 
Sine 1 


.32557 
Cosin 


.94552 
Sine 


.34202 
Cosin 


.93969 
Sine 





Cosin 


Sine 


74° 


73° 1 


72° 


71° 1 


70°. 1 



SINES AND COSINES. 



46? 



~0 


20° 1 


21° I 


22° 1 


230 I 


24° 


/ 
60 


Sine 


Cosin 


Sine 
.35837 


Cosin 
^93358 


Sine 


Cosin 


Sine 


Cosin 


Sine Cosin 
.40674 L 91355 


.34202 


.93969 


.37461 


.'92718 


.39073 


.92050 


1 


.34229 


.93959 


.35864 


.93348 


.37488 


.92707 


.39100 


.92039 


.40700 


.91343 


59 


2 


.34257 


.93949 


.35891 


.93337 


.37515 


.92697 


.39127 


.92028 


.40727 


.91331 


53 


3 


.34284 


.93939 


.35918 


.93327 


.37542 


.92686 


.39153 


.92016 


.40753 


.91319 


57 


4 


.34311 


.93929 


.35945 


.93316 


.37569 


.92675 


.39180 


.92005 


.40780 


.91307 


50 


5 


.34339 


.93919 


.35973 


.93306 


.37595 


.92664 


.39207 


.91994 


.40806 


.91295 


55 


6 


.34366 


.93909 


.36000 


.93295 


.37622 


.92653 


.39234 


.91982 


.40833 


.91283 


51 


7 


.34393 


.93899 


.36027 


.93285 


.37649 


.92642 


.39260 


.91971 


.40860 


.91272 


53 


8 


.34421 


.93889 


.36054 


.93274 


.37676 


.92631 


.39287 


.91959 


.40886 


.91260 


52 


9 


.34448 


.93879 


.36081 


.93264 


.37703 


.92620 


.39314 


.91948 


.40913 


.91248 


51 


10 


.34475 


.93869 


.86108 


.93253 


.37730 


.92609 


.39341 


.91936 


.40939 


.91236 


50 


11 


.34503 


.93859 


.36135 


.93243 


.37757 


.92598 


.39367 


.91925 


.40966 


.91224 


49 


12 


.34530 


.93849 


.36162 


.93282 


.37784 


.92587 


.39394 


.91914 


.40992 


.91212 


43 


13 


.34557 


.93839 


.36190 


.93222 


.37811 


.92576 


.39421 


.91902 


.41019 


.91200 


47 


14 


.34584 


.93829 


.36217 


.93211 


.37838 


.92565 


.39448 


.91891 


.41045 


.91188 


46 


15 


.34612 


.93819 


.36244 


.93201 


.37865 


.92554 


.39474 


.91879 


.41072 


.91176 


46 


16 


.34639 


.93809 


.36271 


.93190 


.37892 


.92543 


.39501 


.91868 


.41098 


.91164 


44 


17 


.34666 


.93799 


.30298 


.93180 


.37919 


.92532 


.39528 


.91856 


.41125 


.91152 


43 


18 


.34694 


.93789 


.36325 


.93169 


.37946 


.92521 


.39555 


.91845 


.41151 


.91140 


42 


19 


.34721 


.93779 


.36352 


.93159 


.37973 


.92510 


.39581 


.91833 


.41178 


.91128 


41 


20 


.34748 


.93769 


.36379 


.93148 


.37999 


.92499 


.39608 


.91822 


.41204 


.91116 


40 


21 


.34775 


.93759 


.36406 


.93137 


.38026 


.92488 


.39635 


.91810 


.41231 


.91104 


39 


22 


.34803 


.93748 


.36434 


.93127 


.38053 


.92477 


.39661 


.91799 


.41257 


.91092 


38 


23 


.34830 


.93738 


.36461 


.93116 


.38080 


.92466 


.39688 


.91787 


.41284 


.91080 


37 


24 


.34857 


.93728 


.36488 


.93106 


.38107 


.92455 


.39715 


.91775 


.41310 


.91068 


36 


25 


.34884 


.93718 


.36515 


.93095 


.38134 


.92444 


.39741 


.91764 


.41337 


.91056 


35 


26 


.34912 


.93708 


.36542 


.93084 


.38161 


.92432 


.39768 


.91752 


.41363 


.91044 


34 


27 


.34939 


.93698 


.36569 


.93074 


.38188 


.92421 


.39795 


.91741 


.41390 


.91032 


33 


28 


.34966 


.93688 


.36596 


.93063 


.38215 


.92410 


.39822 


.91729 


.41416 


.91020 


32 


29 


.34993 


.93677 


.36623 


.93052 


.38241 


.92399 


.39848 


.91718 


.41443 


.91008 


31 


30 


.35021 


.93667 


.36650 


.93042 


.38268 


.92388 


.39875 


.91706 


.41469 


.90996 


30 


31 


.35048 


.9365? 


.36677 


.93031 


.38295 


.92377 


.39902 


.91694 


.41496 


.90984 


29 


32 


.35075 


.93647 


.36704 


.93020 


.38322 


.92366 


.39928 


.91688 


.41522 


.90972 


28 


33 


.35102 


.93637 


.36731 


.93010 


.38349 


.92355 


.39955 


.91671 


.41549 


.90960 


27 


34 


.35130 


.93626 


.36758 


.92999 


.38376 


.92343 


.39982 


.91660 


.41575 


.90948 


26 


35 


.35157 


.93616 


.36785 


.92988 


.38403 


.92332 


.40008 


.91648 


.41602 


.90936 


25 


36 


.35184 


.93606 


.36812 


.92978 


.38430 


.92321 


.40035 


.91636 


.41628 


.90924 


24 


37 


.35211 


.93596 


.36839 


.92967 


.38456 


.92310 


.40062 


.91625 


.41655 


.90911 


23 


38 


.35239 


.93585 


.36867 


.92956 


.38483 


.92299 


.40088 


.91613 


.41681 


.90899 


22 


39 


.35266 


.93575 


.36894 


.92945 


.38510 


.92287 


.40115 


.91601 


.41707 


.90887 


21 


40 


.35293 


.93565 


.36921 


.92935 


.38537 


.92276 


.40141 


.91590 


.41734 


.90875 


20 


41 


.35320 


.93555 


.36948 


.92924 


.38564 


.92265 


.40168 


.91578 


.41760 


.90863 


19 


42 


.35347 


.93544 


.36975 


.92913 


.38591 


.92254 


.40195 


.91566 


.41787 


.90851 


18 


43 


.35375 


.93534: 


.37002 


.92902 


.38617 


.92243 


.40221 


.91555 


.41813 


.90839 


17 


44 


.35402 


.935241 


.37029 


.92892 


.38644 


.92231 


.40248 


.91543 


.41840 


.90826 


16 


45 


.35429 


.93514 


.37056 


.92881 


.38671 


.92220 


.40275 


.91531 


.41866 


.90814 


15 


46 


.35456 


.93503 


,37083 


.92870 


.38698 


.92209 


.40301 


.91519 


.41892 


.90802 


14 


47 


.35484 


.93493 


.37110 


.92859 


.38725 


.92198 


.40328 


.91508 


.41919 


.90790 


13 


48 


.35511 


.93483! 


.37137 


.92849 


.38752 


.92186 


.40355 


.91496 


.41945 


.90778 


12 


49 


.35538 


.93472; 


.37164 


.92838 


.38778 


.92175 


.40381 


.91484 


.41972 


.90766 


11 


50 


.35565 


.93462 


.37191 


.92827 


.38805 


.92164 


.40408 


.91472 


.41998 


.90753 


10 


51 


.35592 


.93452 


.37218 


.92816 


.38832 


.92152 


.40434 


.91461 


.42024 


.90741 


9 


52 


.35619 


.93441 


.37245 


.92805 


.38859 


.92141 


.40461 


.91449 


.42051 


.90729 


8 


53 


.35647 


.93431 


.37272 


.92794 


.38886 


.92130 


.40488 


.91437 


.42077 


.90717 


7 


54 


.35674 


.93420 


.37299 


.92784 


.38912 


.92119 


.40514 


.91425 


.42104 


.90704 


6 


55 


.35701 


.93410 


.37326 


.92773 


.38939 


.92107 


.40541 


.91414 


.42130 


.90692 


5 


56 


.35728 


.93400 


.37353 


.92762 


.38966 


.92096 


.40567 


.91402 


.42156 


.90680 


4 


57 


.35755 


.93389 


.37380 


.92751 


.38993 


.92085 


.40594 


.91390 


.42183 


.90668 


3 


58 


.35782 


.93379 


.37407 


.92740 


.39020 


.92073 


.40621 


.91378 


.42209 


.90655 


2 


59 


.35810 


.93368 


.37434 


.92729 


.39046 


.92062 


.40647 


.91366 


.42235 


.90643 


1 


CO 


.35837 


.93358 


.37461 
Cosin 


/J2718 
Sine 


.39073 
Cosin 


.92050 
~Sine~ 


.40674 
Cosin 


.91355 
Sine 


.42262 
Cosin 


.90631 
Sine 





Cosiu 


Sine 


69- 1 


68- 1 


67° 1 


66° 1 


66° 



468 



ST^NTES AND COSTN"ES. 



"o 


25° 


26° 


27° 1 


28° I 


29° 


/ 

60 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


.42262 


.90631 


.43837 


.89879 


.45399 


.89101 


.46947 


.88295 


.48481 


.87462 


1 


.42288 


.90618 


.43863 


.89867 


.45425 


.89087 


.46973 


.88281 


.48506 


.87448 


59 


2 


.42315 


.90606 


.43889 


.89854 


.45451 


.89074 


.46999 


.88267 


.48532 


.87434 


58 


3 


.42341 


.90594 


.43916 


.89841 


.45477 


.89061 


.47024 


.88254 


.48557 


.87420 


57 


4 


.42367 


.90582 


.43942 


.89828 


.45503 


.89048 


.47050 


.882401 


.48583 


.87406 


56 


5 


.423941.90569 


.43968 


.89816 


.45529 


.89035 


.47076 


.88226 


.48608 


.87391 


55 


6 


.424201.90557 


.43994 


.89803 


.45554 


.89021 


.47101 


.88213 


.48634 


.87377 


5-4 


7 


.42446;. 90545 


.44020 


.89790 


.45580 


.89008 


.47127 


.88199 


.48659 


.87363 


53 


8 


. 42473 ;.G0532 


.44046 


.89777 


.45606 


.88995 


.47153 


.88185 


.48684 


.87349 


52 


9 


.42499 


.90520 


.44072 


.89764 


.45632 


.88981 


.47178 


.88172 


.48710 


.87335 


51 


10 


.42525 


.90507 


.44098 


.89752 


.45658 


.88968 


.47204 


.88158 


.48735 


.87321 


50 


11 


.42552 


.90495 


.44124 


.89739 


.45684 


.88955 


.47229 


.88144 


.48761 


.87306 


49 


12 


.42578 .904831 


.44151 


.89726 


.45710 


.88942 


.47255 


.88130 


.48786 


.87292 


48 


13 


.42604 


.90470 


.44177 


.89713 


.45736 


.88928 


.47281 


.88117 


.48811 


.87278 


47 


14 


.42631 


.90458 


.44203 


.89700 


.45762 


.88915 


.47306 


.88103 


.48837 


.87264 


40 


15 


.42657 


.90446 


.44229 


.89687 


.45787 


.88902 


.47332 


.88089 


.48862 


.87250 


45 


16 


.42683 


.90433 


.44255 


.89674 


.45813 


.88888 


.47358 


.88075 


.48888 


.87235 


44 


17 


.42709 


.90421 


.44281 


.896621 


.45839 


.88875 


.47383 


.88062 


.48913 


.87221 


43 


18 


.42736 


.90408 


.44307 


.896491 


.45865 


.88862 


.47409 


.88048 


.48938 


.87207 


42 


19 


.42762 


.90396 


.44333 


.896361 


.45891 


.88848 


.47434 


.88034 


.48964 


.87193 


41 


20 


.42788 


.90383 


.44359 


.89623 


.45917 


.88835 


.47460 


.88020 


.48989 


.87178 


40 


21 


,42815 


.90371 


.44385 


.896101 


.45942 


.88822 


.47486 


.88006 


.49014 


.87164 


30 


22 


.42841 


.90358 


.44411 


.895971 


.45968 


.88808 


.47511 


.87993 


.49040 


.87150 


38 


23 


.42867 


.90346 


.44437 


. 89584 i 


.45994 


.88795 


.47537 


.87979 


.49065 


.87136 


37 


24 


.42894 


.90334 


.44464 


.89571 ' 


.46020 


.88782 


.47562 


.87965 


.49090 


.87121 


36 


25 


.42920 


.90321 


.44490 


.89558 


.46046 


.88768 


.47588 


.87951 


.49116 


.87107 


35 


26 


.42946 


.90309 


.44516 


.895451 


.46072 


.88755 


> .47614 


.87937 


.49141 


.87093 


34 


27 


.42972 


.90296 


.44542 . 89532 : 


.46097 


.88741 


.47039 


.87923 


.49166 


.87079 


33 


28 


.42999 


.90284 


.445GS .89519; 


.46123 


.88728 


.47665 


.87909 


.49192 


.87064 


32 


29 


.43025 


.91271 


.44594 


.89508 


.46149 


.88715: 


.47690 


.87896 


.49217 


.87050 


31 


30 


.43051 


.90259 


.44620 


.89493 


.46175 


.88701 


.47716 


.87882 


.49242 


.87036 


30 


31 


.43077 


.90246 


.44646 


.89480 


.46201 


.88688 


.47741 


.87868 


.49268 


.87021 


29 


32 


.43104 


.90233 


.44672 


.89467 


.46226 


.88674 


.47767 


.87854 


.49293 


.87007 


28 


33 


.43130 


.90221 


.44698 


.89454 


.46252 


.88661 


.47793 


.87840 


.49318 


.86993 


27 


34 


.43156 


.90208; 


.44724 


.89441 


.46278 


.88647, 


.47818 


.87826 


.49344 


.86978 


26 


35 


.43182 


.90196 


.44750 


.89428 


.46304 


.88634' 


.47844 


.87'812 


.49369 


.86964 


25 


30 


.43209 


.90183 


.44776 


.89415 


, .46330 


.88620 


.47869 .87798 


1 .49394 


.86949 


24 


37 


.43235 


.90171 


.44802 


.89402 


.40355 


.88607 


.47895 .87784 


.49419 


.86935 


23 


38 


.43261 


.90158 


.44828 


.89389 


i .46381 


.88593 


.479201.87770 


.49445 


.86921 


22 


39 


.43287 


.90146 


.44854 


.89376 


] .46407 


.88580 


.479461.87756 


.49470 


.86906 


21 


40 


.43313 


.90133 


.44880 


.89363 


i .46433 


.88566 


.47971 L 87743 


.49495 


.86892 


20 


41 


.43340 


.90120 


.44906 


.89350 


.46458 


.88553 


.47997 .87729 


.49521 


.86878 


19 


42 


.43366 


.90108 


.44932 


.89337 


.46484 


.88539 


.48022 '.87715 


.49546 


.86863 


18 


43 


.43392 


.90095 


.44958 


.89324 


.46510 


.88526 


.48048 .87701 


.49571 


.86849 


17 


44 


.43418 


.90082 


.449841.89311 


.46536 


.88512 


.48073 .87687 


.49596 


.86834 


16 


45 


.43445 


.90070: 


.45010;. 89298 


.46501 


.88499 


.48099 .87673 


.49622 


.86820 


15 


46 


.43471 


.90057 


.45036 .89285 


.46587 


.88485 


.48124 .87659 


.49647 


.86805 


14 


47 


.43497 


.90045: 


.45062 


.89272 


.46613 


.88472 


.48150. 87645 


.49672 


.86791 


13 


48 


.43523 


.90032! 


.45088 


.89259 


.46639 


.8^458 


.481751.87631 


.49697 


.867VV 


12 


49 


.43549 


.90019 


.45114 


.89245 


.46664 


.88445 


.482011.87017 


.49723 


.86762 


11 


50 


.43575 


.90007 


.45140 


.89232 


.46690 


.8&431 


.48226 


.87603 


.49748 


.86748 


10 


51 


.43602 


.89994 


.45166 


.89219 


.46716 


.88417 


.48252 


.87589 


.49773 


.86733 


9 


52 


.4:^628 


.89981 


.45192 


.89206 


.46742 


.88404 


.48277 


. 87575 


.49798 


.86719 


8 


53 


.43654 


.89968 


.45218 


.89193 


.46767 


.88390 


.4a303 


.87561 


.49824 


.86704 


7 


54 


.4:3680 


.899561 


.45243 


.89180 


.46793 


.88377 


.48328 


.87546 


.49849 


.86690 


6 


55 


.43706 


.8994:31 


.45269 


.89167 


.46819 


.88363 


.48354 


.87532 


.49874 


.86675 


5 


56 


.43733 


.89930' 


.45295 


.89153 


.46844 


.88349 


.48379 


.87518; 


.49899 


.86661 


4 


57 


.43759 


.89918 


.45321 


.89140 


.46870 


.88336 


.48405 


.87504: 


.49924 


.86646 


3 


58 


.43785 


.89905; 


.45347 


.89127 


.46896 


.88322 


.48430 


.874901 


.49950 


.86632 


2 


59 


.43811 


.89892 


.45373 


.89114 


.46921 


.88:308 


.48456 


.87476 


.49975 


.86617 


1 


60 


.43837 


.89879 


.451399 


.89101 


1 .46947 


.88295 


.48481 


.87462 


.50000 


.86603 


_0 

/ 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin Sine 1 


Cosin 


Sine 


64° 1 


63° 1 


1 6S 


l!° 


61 


o 1 


60° 1 



SINES AND COSINES. 



469 



"o 


30» 1 


3P I 


32° 1 


33° 1 


34° 1 


60 


Sine 

.50000 


Cosin 

.86603 


Sine 
.51504 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


.85717 


.52992 


.84805^ 


.54464 


.83867 


.55919 


.82904 


1 


.50025 


.86588 


.51529 


.85702 


.53017 


.84789; 


.54488 


.83851 


.55943 


.82887 


59 


2 


.50050 


.86573 


.51554 


.85687 


.53041 


.847741 


.54513 


.83835 


.55968 


.82871 


58 


3 


.50076 


.86559 


.51579 


.85672 


.53066 


.84759 


.54537 


.83819 


.55992 


.82855 


67 


4 


.50101 


.86544 


.51604 


.85657 


.53091 


.84743 


.54561 


.83804 


.56016 


.82839 


53 


5 


.50126 


.86530 


.51628 


.85642 


.53115 


.84728 


.54586 


.83788 


.56040 


.82822 


55 


6 


.50151 


.86515 


.51653 


.85627 


.53140 


.84712 


.54610 


.83772 


.56064 


.82806 


5i 


7 


.50176 


.86501 


.51678 


.85612 


.53164 


.84697 


.54635 


.83756 


.56088 


.82790 


53 


8 


.50201 


.86486 


.51703 


.85597 


.53189 


.84681 


.54659 


.83740 


.56112 


.82773 


52 


9 


.50227 


.86471 


.51728 


.85582 


.53214 


.84666 


.54683 


.83724 


.56136 


.82757 


r ! 


10 


.50252 


.86457 


.51753 


.85567 


.53238 


.84650! 


.54708 


.83708 


.56160 


.82741 


50 


11 


.50277 


.86442 


.51778 


.85551 


.53263 


.84635 


.54732 


.83692 


.56184 


.82724 


&D 


12 


.50302 


.86427 


.51803 


. 8553G 


. 53283 


.84619 


.54756 


.83676 


.56208 


.82708 


/3 


13 


.50327 


.86413 


.51828 


.85521 


.53312 


.84604 


.54781 


.83660 


.56232 


.82692 


47 


14 


.50352 


.80398 


.51852 


.85506 


.53337 


.84588 


.54805 


.83645 


.56256 


.82675 


40 


15 


.50377 


.86384 


.51877 


.85491 


.53361 


.84573 


.54829 


.83629 


.56280 


.82659 


^"j 


16 


.50403 


.86369 


,51902 


.85476 


.53386 


.84557 


.54854 


.83613 


.56305 


.82643 


44 


17 


.50428 


.86354 


.51927 


.85461 


.53411 


.84542 


.54878 


.83597 


.56329 


.82626 


43 


18 


.50453 


.86340 


.51952 


.85446 


.53435 


.84526 


.54902 


.83581 


.56353 


.82610 


42 


19 


.50478 


.86325 


.51977 


.85431 


.534G0 


.84511 


.h4927 


.83565 


.56377 


.82593 


41 


20 


.50503 


.86310 


.52002 


.85416 


.53^184 


.84495 


.54951 


.83549 


.56401 


.82577 


40 


21 


.50528 


.86295 


.52026 


.85401 


.53509 


.84480 


.54975 


.83533 


.56425 


.82561 


30 


22 


.50553 


.86281 


.5:3051 


.85385 


.53534 


.84464 


.54999 


.83517 


.56449 


.82544 


H 


23 


.50578 


.86266 


.52076 


.85370 


.53558 


.84448 


.55024 


.83501 


.56473 


.82528 


L/ 


24 


.50603 


.80251 


.52101 


.85355 


.53583 


.84433 


.55048 


.83485 


.56497 


.82511 


ou 


25 


,50628 


.86237 


.52126 


.85340 


.53607 


.84417 


.55072 


.83469 


.56521 


.82495 


35 


26 


.50654 


.86222 


.52151 


.85325 


.53632 


.84402 


.55097 


.83453 


.56545 


.82478 


31 


27 


.50679 


.86207 


.52175 


.85310 


.53656 


.84386 


.55121 


.83437 


.56569 


.82462 


£3 


28 


.50704 


.86192 


.52200 


.85294 


.53681 


.84370 


.55145 


.83421 


.56593 


.82446 


32 


29 


.50729 


.86178 


.52225 


.85279 


.53705 


.84355 


.55169 


.83405 


.56617 


.82429 


31 


30 


.50754 


.86163 


.52250 


.85264 


.53730 


.84339 


.55194 


.83389 


.66641 


.82413 


30 


31 


.50779 


.86148 


.52275 


.85249 


.53754 


.84324 


.55218 


.83373 


.56665 


.82396 


CO 


32 


.50804 


.86133 


.52299 


.85234 


.53779 


.843081 


.55242 


.83356 


.56689 


.82380 


20 


33 


.50829 


.86119 


.52324 


.85218 


.53804 


.842921 


.55266 


.83340 


.56713 


.82363 


C7 


34 


.50854 


.86104 


.52349 


.85203 


.53828 


.84277 


.55291 


.83324 


.56736 


.82347 


r ■> 


35 


.50879 


.86089 


.52374 


.85188 


.53853 


.84261 


.55315 


.83308 


.56760 


.82330 


£5 


36 


.50904 


.86074 


.52399 


.85173 


.53877 


.84245 


.55339 


.83292 


.56784 


.82314 


24 


37 


.50929 


.86059 


.52423 


.85157 


.53902 


.84230 


.55363 


.83276 


.56808 


.82297 


23 


38 


.50954 


.86045 


.52448 


.85142 


.53926 


.842141 


.55388 


.83260 


.56832 


.82281 


£3 


39 


.50979 


.86030 


.52473 


.85127 


.53951 


.84198 


.55412 


.83244 


.56856 


.82264 


£1 


40 


.51004 


86015 


.52498 


.85112 


.53975 


.84182 


.55436 


.83228 


.66880 


.82248 


20 


41 


.51029 


.86000 


.52522 


.85096 


.54000 


.84167 


.55460 


.83212 


.56904 


.82231 


10 


42 


.51054 


.85985 


.52547 


.85081 


.54024 


.84151 


.55484 


.83195 


.56928 


.82214 


13 


43 


.51079 


.85970 


.52572 


.85066 


.54049 


.84135 


.55509 


.83179 


.56952 


.82198 


17 


44 


.51104 


.85956 


.52597 


.85051 


.54073 


.84120 


.55533 


.83163 


.56976 


.82181 


16 


45 


.51129 


.85941 


.52621 


.85035 


.54097 


.84104 


.55557 


.83147 


.57000 


.82165 


15 


46 


.51154 


.85926 


.52646 


.85020 


.54122 


.84088 


.55581 


.83131 


.57024 


.82148 


14 


47 


.51179 


.85911 


.52671 


.85005 


.54146 


.84072 


.55605 


.83115 


.57047 


.82132 


13 


48 


.51204 


.85896 


.52696 


.84989 


.54171 


.84057 


.55630 


.83098 


.57071 


.82115 


1^^ 


49 


.5i229 


.85881 


.527'20 


.84974 


.54195 


.84041 


.55654 


.83082 


.57095 


.82098 


11 


50 


.51254 


.85866 


.52745 


.84959 


.54220 


.84025 


.55678 


.83066 


.57119 


.82082 


10 


51 


.51279 


.85851 


.52770 


.84943 


.54244 


.84009 


.55702 


.83050 


.57143 


.82065 


o, 


52 


.51304 


.85836 


.52794 


.84928 


.54269 


.83994 


.55726 


.83034 


.67167 


.82048 


8 


53 


.51329 


.85821 


.52819 


.84913 


.54293 


.83978 


.55750 


.83017 


.57191 


.82032 


7 


54 


.51354 


.85806 


.52844 


.84897 


.54317 


.83962 


.55775 


.83001 


.57215 


.82015 


C 


55 


.51379 


.85792 


.52869 


.^4882 


.54342 


.83946 


.55799 


.82985 


.67238 


.81999 


5 


56 


.51404 


.85777 


.52893 


.84866 


.54366 


.83930 


.55823 


.82969 


.67262 


.81982 


4 


57 


.51429 


.85762 


.52918 


.84851 


.64391 


.83915 


.55847 


.82953 


.57286 


.81965 


3 


58 


.51454 


.85747 


.52943 


.84836 


.54415 


.83899 


.55871 


.82936 


.57310 


.81949 


'J 


59 


.51479 


.85732 


.52967 


.84820 


.54440 


.83883 


.55895 


.82920 


.67334 


.81932 


1 


60 
/ 


.51504 


.85717 


,52992 


.84805 


.54464 
Cosin 


.83867 
Sine 


.55919 


.82904 


.67368 


.81915 


6 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


Sine 


Cosin 


'Sine' 


69° 


68° 


67° 


66° 


66» 


_j 



470 



SIKES AND COSINES. 



/ 

"o 


35° I 


36° 1 


37° i 


38° 1 


39° 1 




Sine 


Cosin 1 


Sine 

.58779 


Cosin 1 
.80902 


Sine 

.60182 


Cosin 1 
.79804 


Sine ' 
' .61566 


Cosin i 
.78801 


Sine 
.62932 


Cosin 
.77715 


/ 


.57358 


.81915 


60 


1 


.57381 


.81899 


.58802 


.80885 


.60205 


.79846 


.61589 


.7878:3 


.62955 


.77696 


59 


2 


.57405 


.81882 


.58826 


.80867 


.60228 


.79829 


.61612 


.78765 


.62977 


.77678 


58 


3 


.57429 


.81865 


.58849 


.80850 


.60251 


.79811 


.61035 


.78747 


.63000 


.77660 


57 


4 


.57453 


.81848 


.58873 


.80833 


.60274 


.79793 


i .61658 


.78729 


.63022 


.77641 


56 


5 


.57477 


.81832 


.58896 


.80816 


.60298 


.79776 


! .61681 


.78711' 


.63045 


.77623 


55 


6 


.57501 


.81815 


.58920 


.80799 


.60321 


.79758 


i .61704 


.78694' 


.63068 


.77605 


54 


7 


.57524 


.81798 


.58943 


.80782 


.60344 


.79741 


1 .61726 


.78676 


.63090 


.77586 


53 


8 


.57548 


.81782 


.58967 


.80765 


.60367 


.79723 


.61749 


.78658 


.63113 


.77568 


52 


9 


.57572 


.81765 


.58990 


.80748 


.60390 


.79706 


.61772 


.78640 


.63135 


.77550 


51 


10 


.57596 


.81748 


.59014 


.80730 


.60414 


.79688 


.61795 


.78622 


.63158 


.77531 


50 


11 


.57619 


.81731! 


.59037 


.80713 


.60437 


.79671 


.61818 


.786041 


.63180 


.77513 


40 


12 


.57643 


.81714' 


.59061 


.80696 


.60460 


.79653 


.61841 


.78586 


.63203 


.77494 


48 


13 


.57667 


.81698 


.59084 


.80679 


.60483 


.79635 


1 .G1864 


.78568 


.63225 .77476 


47 


14 


.57691 


.81681' 


.59108 


.80662 


.60506 


.79618 


.61887 


.78550 


.63248 .77458 


46 


15 


.57715 


.81664 


.59131 


.80644 


.60529 


.79600 


.61900 


.78532 


.63271 .77439 


45 


16 


.57738 


.81647 


.59154 


.80627 


.60553 


.79583 


.61932 


.78514 


.63293 .77421 


44 


17 


.57762 


.81631 


.59178 


.80610 


.60576 


.79565 


.61955 


.78496 


.63316 .77402 


42 


18 


.57786 


.81614 


.59201 


.80593 


.60599 


.79.>47 


.61978 


.7^78 


.63338 .77384 


42 


19 


.57810 


.81597 


.59225 


.80576 


.60622 


.79530 


i .62001 


.78460 


.63361 .77366 


41 


20 


.57833 


.81580; 


.59248 


.80558 


.60645 


.79512 


' .62024 


.78442 


.63383 .77347 


4C 


21 


.57857 


.81563' 


.59272 


.80541 


.60668 


.79494 


.62046 


.78424' 


'.6^406'. 77329 


3£ 


22 


.57881 


.81546 


.59295 


.80524 


.60691 


.79477 


.62069 


.78405 


.63428 .77310 


3$ 


23 


.57904 


.81530 


■ .59318 


.80507 


.60714 


.79459 


.62092 


.78387 


.63451 .77292 


37 


24 


.57928 


.81513 


.59342 


.80489 


.60738 


.79441 


.62115 


.7a369 


.63473 .77273 


36 


25 


.57952 


.81496 


' .59365 


.80472 


.60761 


.79424 


.62138 


.78351 


1 .63496 .77255 


35 


26 


.57976 


.81479 


.59389 


.80455 


.60784 


.79406 


.62160 


.7833:3 


! .63518 .77236 


S4 


27 


.57999 


.81462 


; .59412 


.80438 


.60807 


.79388 


.62183 


.7^315 


' .63540 .77218 


33 


28 


.58023 


.81445 


.59436 


.80420 


1 .60830 


.79371 


.62206 


.78297 


.63563 .77199 


32 


29 


.58047 


.81428 


.594.59 


.80403 


i 60853 


.793.53 


.62229 


.78279 


.63585 .77181 


31 


30 


.58070 


.81412 


1 .59482 


.80386 


.60876 


.79^35 


.62251 


.78261 


.63608 .77162 


30 


31 


.58094 


.81395 


.59506 


.80368 


.60899 


.79318 


.62274 


'.78243 


.63630 .77144 


29 


32 


.58118 


.81378 


.59529 


.8a351 


.60922 


.79300 


.62297 


.78225 


.63653 .77125 


28 


33 


.58141 


.81361, 


.59552 


.80334 


' .60945 


.79282 


.62320 


.78206 


.63675 .77107 


27 


34 


.58165 


.81344 


' .59576 


.80316 


' .60968 


.79264 


.62342 


.78188 


.63698 .77088 


26 


35 


.58189 


.813271 


; .59599 


.80299 


, .60991 


.79247 


.62365 


.78170 


t .63720 .77070 


25 


36 


.58212 


.81310' 


I .59622 


.80282 


.61015 


.79229 


.62:388 


.78152 


.63742 .77051 


24 


37 


.58236 


.812931 


, .59646 


.80264^ 


.61038 


.79211 


.62411 


.78134 


i .63765 .77033 


23 


38 


.58260 


.81276 


.59069 


.80247 


.61061 


.79193 


.62433 


.78116 


' .63787 .77014 


22 


39 


.58283 


.812.59 


.59693 


.80230 


' .61084 


.79176 


.62456 


.78098 


' .63810 .76996 


21 


40 


.58307 


.81242. 


.59716 


.80212 


i .61107 


.79158 


.62479 


.78079 


.63832 .76977 


26 


41 


.5a330 


. 81225 ' 


! .59739 


.80195' 


i .61130 


.79140 


'.62502 


.78061 


.638541.76959 


19 


42 


.58.3.54 


.81208 


1 .59763 


.80178 


1 .61153 


.79122 


.62524 


.78043 


.63877 .76940 


18 


43 


.58378 


.81191 


1 .597.86 


.80160 


I .61176 


.79105 


.62547 


.78025 


; .63899 .76921 


17 


44 


.58401 


.81174 


1 .59809 


.80143 


! .61199 


.79C87 


.62570 


.78007 


.63922 .76903 


16 


45 


.58425 


.81157 


1 .59832 


.80125! 


.61222 


.79069 


.62592 


.77988 


I .63944 .76884 


15 


46 


.58449 


.81140 


1 .59856 


.80108 


.61245 


.79051 


.62615 


.77970 


! .63966 .76866 


14 


47 


.58472 


.81123 


j .59879 


.80091 


.61268 


.790:33 


.62638 


.77952 


.63989 .76^7 


13 


48 


.58496 


.81106 


! .59902 


.80073 


.61291 


.79016 


.62660 


.77934 


.64011 .76828 


12 


49 


.58519 


.81089 


i .59926 


.80056 


.61314 


.78998 


.62683 


.77916 


.&40:33 .76810 


11 


50 


.58543 


.81072 


i .59949 


.80038; 


.6ia37 


.78980 


.62706 


.77897, 


.64056 .76791 


10 


51 


.5a567 


.81055! 


.59972 


.80021' 


.61360 


.78962 


j. 62728 


.VV8'<9; 


.64078 .76772 


9 


52 


.58590 


.810:B8 


.59995 


.80003 


.61383 


.78944 


' .62751 


.77861 


.64100 .76754 


8 


53 


.58614 


.81021 


: .60019 


.79986 


.61406 


.78926 


' .62774 


.77843 


.&4123 .76735 


7 


54 


. 586^^7 


.81004 


.60042 


.79968 


.61429 


.78908 


1 .62796 


.77824 


.64145 .70717 


6 


55 


.58661 


.80987 


.60065 


.79951 


.61451 


.78891 


.62819 


.77806 


.&4167 .76698 


5 


56 


.58684 


.80970 


! .60089 


.799:i4 


.61474 


.78873 


.62^2 


.77788 


.64190 '.76679 


4 


57 


.58708 


.809.53 


.60112 


.79916 


.61497 


.78855 


.62864 


.77769 


.64212 .76661 


3 


58 


.58731 


.80936 


: .60135 


.79899 


.61520 


.78837 


.62887 


.77751 


.64234 .76642 


2 


59 


.58755 


.80919 


1 .60158 


.79881 


.61543 


.78819 


1 .62909 


.77733 


.64256 .76623 


1 


60 


.58779 
Cosin 


.80902 
Sine 1 


1 .60182 
Cosin 


.79864 
Sine' 


^61566 
Cosin 


.78801 
Sine 


1.62932 
j Cosin 


.77715 
Sine 


.64279 .76604 





Cosin i Sine 


/ 


54° 


63° 


62° 


61° 1 


50° 





SINES AND COSINES. 



471 





40° 


41° 


42° 


40° 


440 


/ 
60 


/ 


Sine 


Cosin 
.76604 


Sine 
.65606 


Cosin 


Sine 
.66913 


Cosin 
.74314 


Sine 
.68200 


Cosin 
.73135 


Gine 
.69466 


Cosin 


~0 


.64279 


.75471 


1 


.64301 


.76586 


.65628 


.75452 


.66935 


.74295 


.68221 


.73110 


.69487 


.71914 


50 


2 


.64323 


.76567 


.65650 


.75433 


.66956 


.74276 


.68242 


.73096 


.69508 


.71894 


53 


3 


.64346 


.76548 


.65672 


.75414 


.60978 


.74256 


.68264 


.73076 


.69529 


.71873 


57 


4 


.64368 


.76530 


.65694 


.75395 


.60999 


.74237 


.68285 


.73056 


.69549 


.71853 


53 


5 


.64390 


.76511 


.65716 


.75375 


.67021 


.74217 


.68306 


.73036 


.69570 


.71833 


55 


6 


.64412 


.76492 


.65738 


.75353 


.67043 


.74198 


.68327 


.73016 


.69501 


.71813 


5i 


7 


.64435 


.76473 


.65759 


.75337 


.67064 


.74178 


.68349 


.72096 


.69012 


.71792 


5'] 


8 


.64457 


.76455 


.65781 


.75318 


.67086 


.74159 


.68370 


.72976 


.69083 


.71772 


5J 


9 


.64479 


.76436 


.65803 


.75299 


.67107 


.74139 


.68391 


.72957 


.69654 


.71752 


51 


10 


.64501 


.76417 


.65825 


.75280 


.67129 


.74120 


.68412 


.72937 


.69675 


.71732 


50 


11 


.64524 


.76398 


.65847 


.75261 


.67151 


.74100 


.68434 


.72917 


.69696 


.71711 


40 


u 


.64546 


.73380 


.65330 


.75241 


.67172 


.74080 


.68455 


.72897 


.69717 


.71691 


43 


13 


.64568 


.76361 


.65891 


.75222 


.67194 


.74061 


.68476 


.72877 


.69737 


.71671 


47 


14 


.64590 


. 76342 


.65913 


.75203 


.67215 


.74041 


.68497 


.72857 


.C97'58 


.71650 


40 


15 


.64612 


.76323 


.65935 


.75184 


.67237 


.74022 


.68518 


.72837 


.69779 


.71630 


45 


16 


.64635 


.76304 


.65956 


.75165 


.67258 


.74002 


.68539 


.72817 


.69800 


.71610 


44 


17 


.64657 


.76286 


.65378 


.75146 


.67280 


.73983 


.68561 


.72797 


.60821 


.71590 


43 


18 


.64679 


.76267 


.66000 


.75123 


.67301 


.73963 


.68582 


.72777 


.69842 


.71569 


42 


19 


.64701 


.76248 


.66022 


.75107 


.67323 


.73944 


.68603 


.72757 


.60362 


.71549 


41 


20 


.64723 


.76229 


.66044 


.75088 


.67344 


.73924 


.68624 


.72737 


.69883 


.71529 


40 


21 


.64746 


.76210 


.66066 


.75069 


.67366 


.73904 


.68645 


.72717 


.69904 


.71508 


39 


22 


.64768 


.76192 


.66038 


.75050 


.67387 


.73885 


.68666 


.72697 


.69925 


.71488 


38 


23 


.64790 


.76173 


.66109 


.75030 


.67409 


.73865 


.68688 


.72677 


.69946 


.71468 


37 


24 


.64812 


.76154 


.66131 


.75011 


.67430 


.73846 


.68709 


.72657 


.69966 


.71447 


36 


25 


.64834 


.76135 


.66153 


.74992 


.67452 


.73826 


.68730 


.72637 


.69987 


.71427 


35 


26 


.64856 


.76116 


.66175 


.74973 


.67473 


.73806 


.68751 


.72617 


.70008 


.71407 


34 


27 


.64878 


.76097 


.66197 


.74953 


.67495 


.73787 


.68772 


.72597 


.70029 


.71386 


33 


28 


.64901 


.76078 


.68218 


,74934 


.67516 


.73767 


.68793 


.72577 


.70049 


.71366 


32 


29 


.64923 


.76059 


.66240 


.74915 


.67538 


.73747 


.68814 


.72557 


.70070 


.71345 


31 


30 


.64945 


.76041 


.66262 


.74896 


.67559 


.73728 


.68835 


.72537 


.70091 


.71325 


30 


31 


.64967 


.76022 


.66284 


.74876 


.67580 


.73708 


.68857 


.72517 


.70112 


.71305 


29 


32 


.64989 


.76003 


.66306 


.74857 


.67602 


.73688 


.68878 


.72497 


70132 


.71284 


28 


33 


.65011 


.75984 


.66327 


.74838 


.67623 


.73669 


.68899 


.72477 


.70153 


.71264 


27 


34 


.65033 


.75965 


.66349 


.74818 


.67645 


.73649 


.68920 


.72457 


.70174 


.71243 


26 


35 


.65055 


.75946 


.66371 


.74799 


.67666 


.73629 


.68941 


.72437 


.70195 


.71223 


35 


36 


.65077 


.75927 


.66393 


.74780 


.67688 


.73610 


.68962 


.72417 


.70215 


.71203 


24 


37 


.65100 


.75908 


.66414 


.74760 


.67709 


.73590 


.68983 


.72397 


.70236 


.71182 


23 


38 


.65122 


.75889 


.66436 


.74741 


.67730 


, 73570 


.69004 


.72377 


.70257 


.71162 


22 


39 


.65144 


.75870 


.66458 


.74722 


.67752 


.73551 


.69025 


.72357 


.70277 


.71141 


21 


40 


.65166 


.75851 


.66480 


.74703 


.67773 


.73531 


.69046 


.72337 


.70298 


.71121 


20 


41 


.65188 


.75832 


.66501 


.74683 


.67795 


.73511 


.69067 


.72317 


.70319 


.71100 


19 


42 


.65210 


.75813 


.66523 


.74664 


.67816 


.73491 


.69088 


.72297 


.70339 


.71080 


18 


43 


.65232 


.75794 


.66545 


.74644 


.67837 


.73472 


.69109 


.72277 


.70360 


.71059 


17 


44 


.65254 


.75775 


.66566 


.74625 


.67859 


.73452 


.69130 


.72257 


.70381 


.71039 


16 


45 


'.65276 


.75756 


.66588 


.74606 


.67880 


.73432 


.69151 


.72236 


.70401 


.71019 


15 


46 


.65298 


.75738 


.66610 


.74586 


.67901 


.73413 


.69172 


.72216 


.70422 


.70998 


14 


47 


.65320 


.75719 


.66632 


.74567 


.67923 


.73393 


.69193 


.72196 


.70443 


.70978 


13 


48 


.65342 


.75700 


.66653 


.74548 


.67944 


.73373 


.69214 


.72176 


.70463 


.70957 


12 


49 


.65364 


.75680 


.66675 


.74528 


.67965 


.73353 


.69235 


.72156 


.70484 


.70937 


11 


50 


.65386 


.75661 


.66697 


.74509 


.67987 


.73333 


.69256 


.72136 


.70505 


.70916 


10 


51 


.65408 


.75642 


.66718 


.74489 


.68008 


.73314 


.69277 


.72116 


.70525 


.70896 


9 


52 


.65430 


.75623 


.66740 


.74470 


.68029 


.73294 


.69298 


.72095 


.70546 


.70875 


8 


53 


.65452 


.75604 


.66762 


.74451 


.68051 


.73274 


.69319 


.72075 


.70567 


.70855 


7 


54 


.65474 


.75585 


.66783 


.74431 


.68072 


.73254 


.69340 


.72055 


.70587 


.70834 


6 


55 


.65496 


.75566 


.66805 


.74412 


.68093 


.73234 


.69361 


.72035 


.70608 


.70813 


5 


56 


.65518 


.75547 


.66827 


.74392 


.68115 


.73215 


.69382 


.72015 


.70628 


.70793 


4 


57 


.65540 


.75528 


.66848 


.74373 


.68136 


.73195 


.69403 


.71995 


.70649 


.70772 


3 


58 


.65562 


.75509 


.66870 


.74353 


.68157 


.73175 


.69424 


.71974 


.70670 


.70752 


2 


59 


.65584 


.75490 


.66891 


.74334 


.68179 


.73155 


.69445 


.71954 


.70690 


.70731 


1 


60 


.65606 
Cosin 


.75471 
Sine 


.66913 .74314 
Cosin Sin© 


.68200 


.73135 


.69466 
Cosin 


.71934 
Sine 


.70711! 


.70711 





/ 


Cosin 


Sine 


Cosin 1 Sine 1 




41 


J° 


4 


B° 


4 


70 


4( 


5° 1 


4S 


,' 1 



4'?2 



SECANTS AND COSECANTS. 



r 






Secants. 






/ 


0" 


r 


2' 


3° 


4^* 


5^ 





1-0000000 


1-0001523 


1-0006095 


1-0013723 


1-0024419 1 


•0038198 


60 


1 


1-0000000 


1-0001574 


1-0006198 


1 0013877 


10024623 3 


•0038454 


69 


2 


1-0000002 


1 -0001627 


1 0006300 


10014030 


10024829 3 


-0038711 


58 


3 


1-0000004 


1 -0001679 


1-0006404 


1-0014185 


1 0025035 1 


■0038969 


57 


4 


1-0000007 


1-0001733 


1-0006509 


10014341 


1 0025241 1 


•0039227 


66 


e 


1-0000011 


1-0001788 


1-0006614 


1-0014497 


10025449 ] 


L -0039486 


65 


6 


1-0000035 


1-0001843 


1-0006721 


1-0014655 


1-0025658 ] 


L -0039747 


54 


7 


1-0000021 


1-0001900 


1-0006828 


1-0014813 


1-0025867 ] 


L 0040008 


63 


8 


1-0000027 


1-0001957 


1-0006936 


1-0014972 


10026078 ] 


L -0040270 


62 


9 


1-0000084 


1-0002015 


1-0007045 


1-0015132 


1-0026289 ] 


L -0040533 


51 


10 


1-0000042 


1-0002073 


1-0007154 


i -0015293 


10026501 ] 


L 0040796 


50 


11 


1-0000051 


1-0002133 


1-0007265 


1-0015454 


1-0026714 1 


L -0041061 


49 


12 


1-0000061 


1-0002194 


1-0007376 


1-0015617 


1-0026928 ] 


L -0041326 


48 


13 


1-0000072 


1-0002255 


1-0007489 


1-0015780 


1-0027142 3 


L -0041592 


47 


14 


1-0000083 


1-0002317 


1-0007602 


1-0015944 


1-0027358 3 


L -0041859 


46 


15 


1-0000095 


1-0002380 


1-0007716 


1-0016109 


1-0027574 3 


L -0042127 


45 


16 


1-0000108 


1-0002444 


1-0007830 


1-0016275 


1-0027791 ] 


L -0042396 


44 


17 


1-0000122 


1-0002509 


1-0007946 


1-0016442 


1-OO280O9 ] 


1-0042666 


43 


18 


1-0000137 


1-0002575 


1-0008063 


1-0016609 


1-0028228 3 


L -0042937 


42 


19 


1-0000153 


1-0002641 


1-0008180 


1-0016778 


1-0028448 3 


L -0043208 


41 


20 


1-0000169 


1-0002708 


1-0008298 


1-0016947 


1-0028669 ] 


L -0043480 


40 


21 


1-0000187 


1-0002776 


1-0008417 


1-0017117 


1-0028890 ] 


L -0043753 


39' 


22 


1-0000205 


1-0002845 


1-0008537 


1-0017-288 


1-0029112 ] 


L -0044028 


38 


23 


1-0000224 


1-0002915 


1-0008653 


1-0017460 


1-0029336 ] 


L -0044302 


37 


24 


1-0000244 


1-0002986 


1-0008779 


1-0017633 


1-0029560 ] 


1-0044578 


36 


25 


1-0000264 


1-0003058 


1-0008902 


1-0017806 


1-0029785 


L -0044855 


35 


26 


1 -0000286 


1-0003130 


1-0009025 


1-0017981 


1-0030010 ] 


L -0045132 


34 


27 


1-0000308 


1-0003203 


1-0009149 


1-0018156 


1-0030237 ] 


1-0045411 


33 


28 


1-0000332 


1-0003277 


1-0009274 


1-0018332 


1-0030464 ] 


L -0045690 


32 


29 


1-0000356 


1-0003352 


1-0009400 


1-0018509 


1-0030693 ] 


L -0045970 


31 


30 


1-0000381 


1-0003428 


1-0009527 


1-0018687 


1-0030922 : 


1-0040251 


30 


31 


l-00«0407 


1-0003505 


1-0009654 


1-0018866 


1-0031152 ] 


1-0046533 


29 


32 


1-0000433 


1-0003582 


1-0009783 


1-0019045 


1-0031383 ] 


L -004681 5 


28 


33 


1-0000461 


1-0003660 


1-0009912 


1-0019225 


1-0031615 ] 


L -0047099 


27 


34 


1-0000489 


1-0003739 


1-0010042 


1-0019407 


1-0031847 ] 


1-0047383 


26 


35 


1-0000518 


1-0003820 


1-0010173 


1-0019589 


1-0032081 ] 


L -0047069 


25 


36 


1-0000548 


10003900 


1-0010305 


1-0019772 


1-0032315 ] 


L -0047955 


24 


37 


1-0000579 


1-0003982 


1-0010438 


1-0019956 


1-0032551 


1-0048242 


23 


38 


1-0000611 


1-0004065 


1-0010571 


1-0020140 


1-0032787 ] 


L -0048530 


22 


39 


1-0000644 


1-0004148 


1-0010705 


1-0020326 


1-0033024 ] 


L -0048819 


21 


40 


1-0000677 


1-0004232 


1-0010841 


1-0020512 


1-0033261 ^ 


L -0049108 


20 


41 


1-0000711 


1-0004317 


1-0010977 


1-0020699 


1-0033500 ] 


1-0049399 


19 


42 


1-0000746 


1-0004403 


1-0011114 


1-0020887 


1-0033740 ] 


L -0049690 


18 


43 


1-0000782 


1-0004490 


1-0011251 


1-0021076 


1-00339S0 ] 


L -0049982 


17 


44 


1-0000S19 


1-0004578 


1-0011390 


1-0021266 


1-0034221 : 


L -0050275 


18 


45 


1-0000857 


1-0004066 


1-0011529 


1-0021457 


1-0034463 ' 


L -0050569 


15 


46 


1-0000895 


1-0004756 


1-0011670 


1-0021648 


1-0034706 


1-0050864 


14 


47 


1-0000935 


1-0004846 


1-0011811 


10021841 


1-0034950 


1-0051160 


13 


48 


1-0000975 


1-0004937 


1-0011953 


1-0022034 


1-0035195 


1-0051456 


12 


49 


1-0001016 


1-0005029 


1-0012096 


1-002-2228 


1-0035440 


1-0051754 


11 


60 


1-0001058 


1-0005121 


1-0012239 


1-0022423 


1-0035687 


1-0052052 


10 


51 


1-0001101 


1-0005215 


1-0012384 


1-0022613 


1-0035934 


1-0052351 


9 


52 


1-0001144 


1-0005300 


1-0012529 


1-002-2815 


1-0036182 


1-0052651 


8 


53 


1-0001189 


1-0005405 


1-0012676 


1-00-23013 


1-0036431 


1-0052952 


7 


64 


1-0001234 


1-0005501 


1-0012823 


1-0023211 


1-00366S1 


1-0053254 


6 


55 


1-0001280 


1-0005598 


1-0012971 


1-0023410 


1-0036932 , 


1-0053557 


5 


56 


1-0001327 


1-0005696 


1-0013120 


1-0023610 


1-0037183 


1-0053860 


4 


57 


1-0001375 


1-0005794 


1-0013269 


1-00-23811 


1-0037436 


1-0054164 


3 


68 


1-0001423 


1-0005894 


1-0013420 


1-0024013 


1-0037689 


1-0054470 


2 


69 


1-0001473 


1-0005994 


1-0013671 


1-0024216 


1-0037943 


1-0054776 


1 


60 


1-0001623 


1*0006096 


1-0013723 


1-0024419 


1-0038198 


1-0055083 





/ 


80«» 


88° 


87° 


86° 


85° 


84° 


/ 






Cosecants. 







SECANTS AND COSECANTS. 



473 



Secants. 





1 

2 
3 

4 
5 

6 
7 
8 
d 

10 

11 
12 
13 
II 
15 

\6 
17 
18 
19 
20 

21 
22 
23 
21 
25 

26 
27 
28 



31 
32 
33 
31 
35 

36 
37 
S8 
39 
40 

41 
42 
43 
44 
45 

IG 
47 
43 
49 
50 

51 

52 
53 
54 
55 

56 

57 
58 



6° 

l-00r)5083 
1-0055391 
1-0055(599 
1-0056009 
1-0056319 
1-0056631 

1-0056043 
1-0057256 
1-0057570 
1-0057885 
1-0058200 

1-0058517 
1-0058834 
1-0059153 
l-00.')9472 
1-0059792 

1-0060113 
1-0000435 
1-0060757 
1-0061081 
1-0061405 

1-0061731 
1-0062057 
1 •006-2384 
1-0002712 
1-0063040 

1-0063370 
1-0063701 
1-0064032 
1-0064364 
1-0064697 

1-0065031 
1-0065366 
1-0065702 
1-0066039 
1-0060376 

1-0060714 
1-0067054 
1-0067394 
1-0067735 
1-006S077 

1-0068419 
1-006S763 
1-0069108 
1-0069453 
1-0069799 

1 '00701 46 
1-0070494 
1-0070843 
1-0071193 
1-0071544 

1-0071895 
1-007224S 
1-007*2601 
1-0072955 
1-0073310 

1-0073666 
1-0074023 
1-0074380 
1-0074739 
1-0075098 

83* 



7* 



1-0075098 
1 ■0075159 
1-0075820 
1-0076182 
1-0076545 
1-0078903 

1 -0077273 

1-0077639 

0078005 

0078372 

■0078741 

•0079110 
•0079180 
0079851 
•0080222 
0080595 

1 

■0081343 
0081718 
•0082094 
•0082471 

■0082849 
•00832-28 
0083607 
0083988 
•0084369 

0084752 
•0085135 
0085519 
0085904 
■0086290 

■0086676 

•0087064 
0087452 
•0087842 
■0088232 



00^9015 
0089408 
0089802 
•0090196 

•0090592 
•0090988 
•0001386 
•0091784 
•0092183 

0092583 
0092984 
0093386 
0093788 
0094192 

•0094596 
■0095(.01 
•0095408 
■0095815 
•0096223 

0096631 
■0097041 
•0097452 
•0097863 
•009b27C 

82^ 



1-0098276 

1-0098689 

1-0099103 

•0099518 

•0099934 

•0100351 

•0100769 
•0101187 
•0101607 
•0102027 
•0102449 

•0102871 
•0103294 
0103718 
•0104143 
•0104568 



■0104995 
•0105422 
•0105851 
0106-280 
0106710 

0107141 
0107573 
0108006 
0108440 
•0108875 

0109310 
•0109747 
0110184 
•01106-22 
•0111061 

-0111501 
0111942 
0112384 
■0112827 
0113270 

0113715 
0114160 
0114606 
•0115054 
■0115502 

•0115951 
•0116100 
0116851 
•0117303 
0117755 

•0118209 
•0118663 
0119118 
•0119575 
0120032 

0120489 
0120948 
•0121408 
•0121869 
0rJ2330 

0122793 
•01-23256 
•01237-20 
0124185 



1^0124651 
10125118 
1^0125586 
1 0126055 
r0126524 
1^012099j 

10127166 
1-0127939 
1-0128412 
1 -01*8886 
i-0129361 

1-0129837 
1 0130314 
1-0130791 
10131-270 
1-0131750 

1-0132230 
1-013-2711 
10133194 
1-0133677 
1-0134161 

10134646 



1-0124651 
81** 



0135132 
0135618 
•0136106 
0136595 

•0137084 
0137574 
•0138066 
0138558 
•0139051 

0139545 
■0140040 
0140536 
•0141032 
0141530 

•0142029 
0142528 
0143028 
■0143530 
0144032 

■0144535 
1145039 
•0145514 
■0146050 
•0146556 

•0147064 
0147572 
0148082 
■0148592 
■0149103 

0H9616 
01501-29 
■0150613 
•0151158 
0151673 

■0152190 
0152708 
0153-J-26 
0153716 
0154266 

80" 



10' 

10154266 
10154787 
1 0155310 
10155833 
10156357 
1-0150882 

10157408 
10157934 
10158462 
10158991 
1-0159520 

1-0160050 
1-0160582 
10161114 
1 0161647 
1-0162181 

1-0162716 
1-0163252 
1-0163789 
1-01643-27 
10161865 

10165405 
1^0165946 
10166487 
1-0167029 
1-0167573 

1-0168117 
1-0168662 
1-0169208 
10169755 
1-0170303 

1-0170851 
1-0171401 
1-0171952 
1-0172503 
1-0173056 

1-0173009 
1-0174163 
10174719 
1-0175-275 
10175832 

1-0176390 
10176949 
1\)177509 
1-0178069 
1-0178681 

10179194 
1-0179757 
1-01803-21 
1-0180887 
1-0181453 

1-0182020 
l-0182r)88 
1-0183158 
1-0183728 
1-0184298 

1-0184870 
1-0185443 
10186017 
10180591 
10187167 

ir 



11** 

10187167 
1-0187743 
1-0188321 
1-0188899 
1-0189478 
1-0190059 

10190640 
101912-22 
1-0191805 
1-0192389 
10192973 

1-0193559 
1-0194146 
1-0194734 
1-0195322 
10195912 

1-0196502 
1-0197093 
1-0197686 
1-0198279 
1-0198873 

1-0199468 
1-0-200064 
1-0200661 
1 •0201259 
1^0201858 

1-0202457 
1-0203058 
1-0203660 
1-0204262 
10204866 

1-0205470 
1-0206075 
1-0-206682 
1-0207289 
rO-207897 

1-0208506 
1 02091 16 
1-0209727 
10210339 
1-0210952 

1-0211506 
10212180 
1^021 2796 
1-0213413 
1-0214030 

1-0214619 
1-0215268 
1-0-215888 
1-0216510 
1-0217132 

1-0217755 
1-0-218379 
1-0219004 
1-0219630 
l-0220-'57 

1 -0220885 
1 02-21 51 4 
10222144 
1-02-22774 
1-0223406 

78** 



57 
56 
55 

54 
63 
52 
51 

50 

49 
43 
47 
46 
45 

44 
43 
42 

41 
40 



37 
36 
35 

34 
33 
32 
31 
30 



27 
26 
25 



22 
21 
20' 

19 
18 
17 
16 
15 

14 
13 
12 
11 
10 



Cosecants. 



474 



SECANTS AND COSECANTS. 



* 






Secants. 






r 


12' 


13* 


14** 


15** 


16' 


17' 




1-0223406 


1-0263041 


1-0306136 


1-0352762 


1-0402994 


1-O45fi018 


60 





1-0224039 


1-0263731 


1-0306884 


1-0353569 


1-0103863 


1-0457848 


59 


1 


1-0224672 


1-0264421 


1-0307633 


1-0354378 


10404732 


1-0458780 


53 


2 


1-0-225307 


10265113 


1-0308383 


1-03^5187 


1-0405602 


1-0459712 


57 


3 
4 
5 

6 

7 
8 
9 
10 


1-0225942 


1-0265806 


1-0309134 


1-0355998 


1-0406473 


1-0460646 


56 


1-0226578 


1-0266499 


1-0309886 


1-0356809 


1-0407346 


1-0461581 


55 


1-0227216 


1-0267194 


1-0310639 


1-0357621 


1-0408219 


1-0462516 


51 


1-0227854 


1-0267889 


1-0311393 


1-0358435 


1-0409094 


1-0463453 


53 


10228493 


1-0268586 


1-031-2147 


10359249 


10409969 


1-0464391 


52 


1-02-29133 


1-0269283 


1-0312903 


1-0360065 


1-0410845 


1-0465330 


51 


1-02-29774 


1-0269982 


1-0313660 


1-0360881 


1-0411723 


10466270 


50 


11 
12 
13 


10230416 


a -0270681 


1-0314418 


10361699 


1-0412601 


1-0467211 


49 


1-0231059 


1-0271381 


1-0315177 


1-036-2517 


1-0413481 


1-0468153 


48 


1-0231703 


1-0272082 


1-0315936 


1-0363337 


1-0414362 


1046^096 


47 


14 


10232348 


1 027-2785 


1-0316U97 


10364157 


1-0415243 


1-0470040 


46 


15 


1-0232994 


1-0273488 


1-0317459 


1-0364979 


1-0416126 


1-0470986 


45 


16 


1-0233641 


1-027419? 


1-0318222 


1-0365S01 


1-0417009 


10471932 


44 


17 


1-0234288 


1-0-274897 


1-0318985 


1-0366625 


1-0417894 


1-0472879 


43 


18 


1-0234937 


1-0275603 


1-0319750 


1-0367449 


1-0418780 


1-0473828 


42 


19 


1-0235587 


1-0276310 


1-0320516 


1-0368275 


1-0419667 


1-0474777 


. 41 


20 


1-0236237 


1-0277018 


1-0321282 


1-0369101 


1-0420554 


10475728 


40 


21 


1-0236889 


1-0277727 


1-0322050 


1-0369929 


1-0421443 


1-0476679 


39 


22 


1-0237541 


1-0278437 


1 -03-22818 


1-0370757 


1-0422333 


1-0477632 


38 


23 


1-0238195 


1-0279148 


1-0323588 


1-0371587 


1-0423224 


1-0478586 


37 


24 


1-0238849 


1-0279860 


1-03-24359 


1-0372417 


1-0424116 


1-0479540 


36 


25 


1-0239504 


1-0280573 


1-03-25130 


1-0373249* 


1-0425009 


1-0480496 


35 


26 


1-0240161 


1-0281287 


1-0325903 


1-0374082 


1-0425903 


10481453 


34 


27 


1-0240818 


1-0-28-20U2 


1-03-26676 


1-0374915 


1-0426798 


1-0482411 


33 


28 


1-0241476 


1-0282717 


1-0327451 


1-0375750 


1-0427694 


1-0483370 


32 


29 


1-0242135 


1-0283434 


1-03282-27 


1-0376585 


1-0428591 


1-048433Q 


31 


SO 


1-0242795 


1-0-284152 


1-0329003 


1-03774-22 


1-0429489 


1-0485291 


30 


31 


1-0243456 


1-0284871 


1-0329781 


1-0378260 


1-04303C3 


1-0486253 


29 


32 


1-0244118 


1-0285590 


1-0330559 


1-0379098 


1-0431289 


1-0487217 


28 


33 


1-0244781 


1-0286311 


1-0331339 


1-0379938 


1-0432190 


1-0488181 


27 


34 


10245445 


1-0287033 


1-0332119 


10380779 


1-0433092 


1-0489146 


26 


35 


1-0246110 


1-0287755 


1-0332901 


1-0381621 


1-0433995 


1-0490113 


25 


36 


1-0246776 


1-0288479 


1-0333683 


1-0382463 


1-0434900 


1-0491080 


24 


37 


1-0247442 


1-0289-203 


1-0334467 


1-0383307 


1-0435805 


1-0492049 


23 


38 


1-0248110 


1-0289929 


1-0335-251 


1-0384152 


10436712 


1-0493019 


22 


39 


1-0248779 


i -0290655 


1-0336037 


1-0384998 


1-0437619 


1-0493989 


21 


40 


1-0210413 


1-02913S3 


1-0336823 


1-0385844 


1-0438528 


10494961 


20 


41 


1-0250119 


1-0292111 


1-0337611 


1-0386692 


1-0439437 


1-0495934 


19 


42 
43 
44 
45 


1-0250790 


1-029-2840 


1-0338399 


1-0387541 


1-0440348 


1-0496908 


18 


1-0251463 


1-0293571 


1-0339168 


1-0388391 


1-0441259 


1-0497883 


17 


1-0252136 


1-0-294302 


1-0339979 


1-0389242 


1-0442172 


1-0498859 


16 


1-0252811 


1-0295034 


1-0340770 


1-0390094 


1-0443086 


1-0499836 


15 


46 
47 
48 
49 
50 


10253486 


1-0295768 


1-0341563 


1-0390947 


1-0444001 


1-0500815 


11 


1-0254162 


1-0296502 


1-0342356 


1-0391800 


1-0444917 


1-0501794 


13 


1-0254839 


10297237 


1-0343151 


1-0392655 


1-0445833 


1-050-2774 


12 


1-0253518 


1-0297973 


1-0343946 


1-0393511 


1-0446751 


1-0503756 


11 


1-0256197 


1-0298711 


1-0344743 


1-0394368 


1-0447670 


1-0504738 


10 


51 
62 


10256877 


1-0299449 


1-0345540 


1-0395226 


1-0448590 


1-0505722 


9 


53 


1-0257558 


1 0300188 


1-0346338 


10396085 


1-0449511 


10506706 


8 


54 


1-0258240 


i -0300928 


1-0347138 


1-0396945 


1-0450433 


1-0507692 


7 


55 


1-0-358923 


1-0301669 


1-0347938 


1-0397806 


10451357 


1-0508679 


6 


56 
57 


1-0259607 


1-0302411 


1-0348740 


1-0398669 


1-0452-281 


1-0509667 


5 


1-0260292 


1-0303154 


1-0349542 


1-0399532 


1-0453206 


1-0510656 


4 


58 


1-0260978 


1-0303898 


10350346 


1-0400396 


1-0454132 


1-0511646 


3 


59 


1-0261665 


1-0304643 


10351150 


1-0401-261 


10455060 


10512637 


8 


60 


1-0262352 


1-0305389 


1:0351955 


1-0402127 


1-0455988 


1-05136-29 


1 




1-0263041 


1-0306136 


1-0352762 


1-0402994 


10456918 


1-0514622 





/ 


ir 


76° 


75** 


74^ 


73'* 


72» 


/ 






Cosecants. 









SECANTS AND COSECANTS. 



475 



t 






Secants. 






_ 

9 


18' 


19' 


20' 


21^ 


22** 


23° 





1-0514622 


1-0576207 


1-0641778 


1-0711450 


10785347 


1-0863604 


60 


1 


10515617 


1-0577267 


1-0642905 


1-0712647 


1-0786616 


1-0864946 


69 


2 


10:)16612 


1 0578323 


1-0644033 


1-0713844 


1-0787885 


1-0866-289 


58 


3 


10517608 


1-0579390 


1-0645163 


1-0715013 


1-0789156 


1-0867634 


57 


4 


1-0518606 


1-0580453 


1-0646-294 


1-0716244 


10790427 


1-0868979 


50 


5 


1-0519605 


10581517 


1-0647425 


1-0717445 


1-0791700 


1-08703-26 


55 


6 


1-0520604 


1-0582583 


1-0648558 


1-0718647 


10792975 


1-0871675 


54 


7 


1-0521605 


1-0583649 


1-0649093 


1-0719851 


1-0794250 


1-0873024 


53 


8 


l-0:>-i2607 


1-0584717 


1-0()50828 


1-0721056 


1-0795527 


1-0874375 


52 


9 


10523610 


1-0585786 


1-0651964 


1-0722262 


1-0796805 


1-0875727 


51 


10 


1-05246U 


1-0586855 


1-0653102 


1-0723469 


1-0798084 


10877080 


50 


11 


10525619 


1-05879-26 


1-0654240 


1-07-24678 


1-0799364 


1-0878435 


49 


12 


l-052()625 


1-0588999 


10655380 


1-0725887 


1-080W546 


1-0879791 


48 


13 


1-0527633 


1-0590072 


1-0656521 


1-0727098 


1-0801928 


1-0881148 


47 


H 


105-28H41 


10591146 


1-0657663 


r07-283l0 


1-0803212 


1-0882506 


46 


15 


1-0529651 


1-0592221 


1-0658807 


1-0729523 


1-0804497 


1-0883866 


45 


16 


1-0530661 


1-0593-298 


1-0659951 


1-0730737 


10805784 


1-0885226 


44 


17 


1-0531675 


1-0594376 


1-0661097 


1-0731953 


1-0807071 


10886589 


43 


18 


1-0532686 


1-0595454 


1-0662-243 


1-0733170 


•10808360 


10887952 


42 


19 


10533699 


1-0596:^4 


1-0663391 


1-0734388 


10809650 


1 0889317 


41 


20 


1-0534714 


1-0597615 


1-0664540 


1-0735607 


1-0810942 


10890682 


40 


21 


10535730 


1-0598697 


1-0665690 


1-0736827 


1-0812234 


1-0892050 


39 


22 


10536747 


1-0599781 


1-0666842 


1-0738048 


1-0813528 


1-0893418 


38 


23 


1-0537765 


1-06008(55 


1-0667994 


1-0739271 


10814823 


1-0894788 


37 


2^ 


1-0538785 


1-0601951 


1-0669148 


10740495 


1-0816119 


1-08S6159 


36 


25 


1-0539805 


10603037 


1-0670302 


1-0741720 


1-0817417 


1-0897531 


35 


26 


10540826 


1-0604125 


1-0671458 


1-0742946 


1-0818715 


1-0898904 


34 


27 


1-0541849 


1-0605214 


1-0672615 


1-0744173 


1-08-20015 


10900279 


33 


28 


1-0542873 


1-0606304 


10673774 


1-0745402 


1-0821316 


1-0901655 


32 


29 


1-0543897 


.1-0607395 


1-0674933 


1-0746631 


1-0822618 


1-0903032 


31 


30 


10544923 


1-0608487 


1-0676094 


1-0747862 


1-0823922 


1-0904412 


30 


31 


1-0545950 


4t 1-0609580 


1-0677255 


1-0749095 


1-0825227 


1-0905791 • 


29 


32 


1-0546978 


1-0610675 


1-0678418 


1-0750328 


1-0826533 


1-0907172 


28 


33 


1-0548007 


1-0611770 


1-0679582 


l•075^562 


1-0827840 


1-0908554 


27 


34 


1-0549037 


1-0612867 


1-0680747 


1-0752798 


1-0829149 


1-0909938 


26 


35 


1-0550063 


1-0613965 


1-0681914 


1-07540S5 


1-0830458 


1-0911323 


25 


36 


1-0551101 


1-0615064 


1-0683081 


1-0755273 


1-0831769 


1-0912709 


24 


37 


1-0552134 


1-0616164 


1-0684250 


1-0756512 


1-0833081 


10914097 


23 


38 


1-0553169 


1-0617265 


1-0685420 


1-0757753 


1-0834395 


1-0915485 


22 


39 


1-0554204 


1-0618367 


1-0686591 


1-0758995 


1-0835709 


1 -0916876 


21 


40 


1-0555241 


1-0619471 


1-0687763 


1-0760237 


10837025 


1-0918267 


20 


41 


1-0556279 


1-0620575 


1-0688936 


1-0761481 


1-0838349 


1-0919659 


19 


42 


10557318 


1-0621681 


1-0690110 


1-0762727 


1-0839661 


1-0921053 


18 


43 


1-0558358 


1-0622788 


1-0691286 


1-0763973 


1-0840980 


1-0922448 


17 


44 


1-0559399 


1-0623896 


1-0692463 


1-0765221 


1-0842301 


1-0923845 


16 


45 


1-0560441 


1-0625005 


1-0693641 


1-0766470 


1-0843623 


1-0925243 


15 


46 


1-0561485 


1-0626115 


10694820 


1-0767720 


1-0844947 


1-0926642 


14 


47 


1-0562529. 


1-0627227 


1-0696000 


1-0768971 


1-0846271 


1-0928042 


13 


48 


1-0563575 


1-0628339 


1-0697182 


1-0770224 


1-0847597 


1-0929444 


12 


49 


1-0564621 


1-0629453 


1-0698364 


1-0771477 


1-0848924 


1-0930846 


11 


50 


10565669 


1-0630568 


10699548 


1-0772732 


1-0850252 


1-0932251 


10 


51 


1-0566718 


1-0631684 


1-0700733 


1-0773988 


1-0851582 


1-0933656 


9 


52 


1-0567768 


1-063-2801 


1-0701919 


1-0775246 


1-0852913 


1-0935063 


8 


53 


1-0568819 


1-0633919 


10703103 


1-0776504 


1-0854245 


1-0936471 


7 


54 


1-0569871 


1-0635038 


1-0704295 


1-0777764 


1-0855578 


1-0937880 


6 


55 


1-0570924 


1-0636158 


1-0705484 


1-0779025 


1-0856912 


1-0939291 


5 


56 


1-0571978 


1-0637280 


1-0706675 


1-0780287 


1-0858248 


1-0940702 


4 


57 


1-0573034 


1-0638403 


1-0707867 


1-0781550 


1-0859585 


1-0942116 


3 


58 


1-0574090 


1-0639527 


1-0709060 


1-0782815 


1-0860924 


1-0943530 


2 


59, 


1-0575148 


1-0640652 


10710254 


1-0784080 


1-0862263 


1-0944946 


1 


60 


1-0576207 


1-0641778 


1-0711450 


1-0785347 


1-0863604 


1-0946363 





/ 

i 


7r 


70' 


69' 


68* 


er 


66* 


/ 






Cosecants. 







476 



SECANTS AND COSECANTS. 



/ 






Secants. 






/ 


24^ 


25° 


26'* 


IT 


28** 


29° 




1 


1-0946363 


110337:9 


1-1126019 


1-1223262 


1-1325701 


1-1433541 


60 


1-0947781 


1-1035277 


1-1127599 


1-1224927 


113-27453 


1-1435385 


50 


1-0949201 


1- 1036775 


1-1129179 


1-1226592 


1-13-29207 


1-1437231 


58 


3 
4 

5 


1 •0950622 


1-103827.5 


1-1130761 


1-1228259 


1-1330962 


1-1439078 


57 


1-09520^4 


1-1039777 


1-1132345 


1-12-29928 


11332719 


1-1440927 


58 


1-0953467 


1-1041279 


1-1133929 


1-1231598 


1-1334478 


1-1442778 


5i^ 


6 
7 
8 
9 
10 


1-0954892 


1-1042783 


1-1135516 


1-1233269 


11336238 


1-1444630 


54 


10956318 


1-1044289 


1*1137103 


1-1234942 


i -1337999 


1-1446484 


53 


1-0957746 


1-1045795 


1-I138(i92 


1-1236616 


1-1339762 


1-1448339 


62 


1-0959174 


1-1047303 


1-1140282 


1-1238-292 


1-1341527 


11450196 


51 


1-0960604 


1-1048813 


1-1141874 


1-1239969 


1-1343293 


1-1452055 


CO 


11 
12 
13 
U 
15 


1-0962036 


1 1050324 


1-1143467 


1-1241618 


1-1345060 


1-1453915 


49 


1-0963468 


1-1051886 


1-1145062 


1-1243328 


1-1346829 


1-1455776 


43 


1 -0964902 


1-1053349 


1-1146658 


1-1245010 


1-1348600 


1-1457639 


47 


1-0966337 


1-1054864 


1-1148255 


1-1246693 


1 1350372 


1-1459504 


46 


1-0967774 


1-1056380 


1-1149854 


1-1248377 


1-135-2146 


1-1461871 


45 


16 


1-0969212 


1-1057898 


1-1151454 


1-1250063 


1-1353921 


1-1463238 


44 


17 


1-0970651 


1-1059417 


1-1153056 


1-1251750 


1-1355697 


1-1465108 


43 


18 


1-0972091 


1-1060937 


1-1154659 


1-1253439 


1-1357476 


1-1466979 


42 


19 


1-0973533 


1-1062453 


1-1156263 


1-1-255130 


1-1359-255 


1-1468852 


41 


SO 


1-0974976 


1-1063981 


1-1157869 


1-1256821 


1-1361036 


1-1470726 


40 


21 


1-0976420 


1-1065506 


1-1159476 


1-1258514 


1-1362819 


1-1472602 


39 


22 


1-0977866 


1-1067031 


1-1161084 


l-1260-.'09 


1-1364603 


1-1474479 


38 
37 


23 
81 


1-0979313 


1-1068558 


1-1162694 


l-12Giy05 


1-I36ti389 


11476358 


10980761 


1-1070087 


1-116430G 


1-1 -263603 


1-1368176 


1-1478-239 


36 


25 


1-0982211 


11071616 


1-1165919 


1-1-265302 


1-1369965 


1-1480121 


35 


20 
27 
28 


1-0983662 


1-1073147 


1-1167533 


1-1267003 


11371755 


i-1482005 


34 


10985114 


1-1074680 


1-1 1691 i8 


1-1268705 


1-1373547 


1-1483890 


33 


1-0986568 


1-107021 t 


1-11707G6 


1-1270408 


1-1375341 


1-H85777 


32 


29 
80 


1-0988023 


1-1077749 


1-1172384 


1-127-2113 


11377135 


1-1487665 


31 


1-0989479 


1-1079285 


1-1174004 


1-1273819 


1-1378932 


1-1489555 


30 


81 


1-099033G 


1-1080823 


1-11756-25 


1-1275527 


1-1380730 


♦ 1-1491447 


29 


82 


1-0992395 


1-1082363 


1-1177248 


1-1277237 


1-1382529 


1-1493340 


23 


33 


1-0993855 


1-1083903 


1-1178872 


1-1278948 


l'138i330 


1-1495235 


27 


31 


1-0995317 


1-1085445 


1-1180498 


1-1280660 


1-1386133 


1-1497132 


26 


35 


1-0996779 


1-1086989 


1-11821-24 


1-1282374 


1-1387937 


1-1499030 


25 


86 


1-0998243 


1-1088533 


1-1183753 


1-1284089 


1-1389742 


1-1500930 


24 


87 


1-0999709 


1-1090079 


1-11853&3 


1-1285806 


1-1391550 


1-150-2831 


23 


88 


1-1001175 


1-1091627 


1-1187014 


1-1287524 


1-1393358 


1-1504734 


22 


39 


1-1002644 


1-1093176 


1-1188647 


1-1289244 


1-1395169 


1-1500638 


21 


iO 


1-1004113 


1-1094726 


1-1190281 


1-1290965 


1-1396980 


1-1508544 


20 


11 


1-10O5584 


1-1096277 


1-1191916 


1-1292687 


1-1398794 


1-1510452 


19 


42 


1-1007056 


1-1097830 


1-1193553 


1-1294412 


1-1400608 


1-1512361 


18 


43 


1-1008529 


1-1099385 


1-1195191 


1-12C6137 


1-14024-25 


1-1514272 


17 


44 


1-1010004 


1-1100940 


M19G831 


1-1297864 


lliU42t3 


1-1516185 


16 


45 


1-1011480 


1-1102498 


1-I198i72 


1-1299593 


1-1406062 


1-1518099 


15 


46 


1-1012957 


1-1104056 


1-1200115 


1-1301323 


1-1407883 


1-1520015 


14 


47 


1-1014436 


1-1105616 


1-1201759 


1-1303055 


1-1409706 


1-1521932 


18 


48 


1-1015916 


1-1107177 


1-1203405 


1-1304788 


1-1411530 


1-1523851 


12 


49 


1-1017397 


1-1108740 


Ml'05O51 


1-1306522 


1-1413356 


1-1525772 


11 


CO 


11018879 


1-11103J4 


1-1206700 


1-1308258 


1-1415183 


1-1527694 


10 


61 


1-1020363 


1-11118G9 


1-1208350 


1-1309995 


1-1417012 


1-1529618 


9 


52 


1-1021849 


1-1113436 


1-1210001 


1-1311735 


1-1418842 


1-1531543 


8 


53 


1-1023335 


1-1115004 


11211653 


11313475 


1-H20674 


11533470 


7 


54 


1-1024823 


11116573 


1-1213308 


1-1315217 


1-142-2507 


11535399 


6 


65 


11026313 


11118144 


M2149G3 


1 1316961 


1-14-24342 


1-1537329 


6 


66 


1-1027803 


1-1119716 


1-1216620 


1-1318706 


1-1426179 


1-1539261 


4 


67 


1-1029295 


1-1121290 


1-1218278 


1-1320452 


1-1428017 


1-1541195 


8 


68 


1-1030789 


1-1122865 


1-1219938 


1-1322200 


1-14-29857 


11543130 


8 


69 


11032283 


11124442 


1-1221600 


1-1323950 


1-1431698 


1-1545067 


1 


60 


11033779 


M12G019 


l-122326i 


1-1325701 


1-1433541 


1-1547005 





/ 


65" 


64" 


63** 


62° 


61" 


60" 


t 






Cosecants. 







SECANTS AND COSECANTS. 



477 










Secants. 






1 


30' 


zv 


32'* 


* 33° 


34*' 


35' 




1-1547005 


1-1666334 


1-1791T84 


1-1923633 


1-2062179 


1-2207746 


60 




1-15 181)45 


1-1668374 


1-1793928 


1-192.3886 


1-2064547 


1-22)0233 


59 




1-156U887 


1-1670410 


1-17^6074 


1-1928142 


1-2066917 


1-2212723 


58 




M 502830 


1-1672459 


1-1798222 


1-1930399 


1-2069288 


1-2215215 


57 




1-1551775 


1 -1674504 


1-1800372 


1-1932658 


1-2071662 


1-2217708 


56 




1-1556722 


Mi;7055i 


1-1802523 


1-1934918 


1-2074037 


1-2220204 


55 




1 •1558(570 


1-1678599 


1-1804676 


1-1937181 


1-2076415 


1-2222702 


54 




1-I5b0629 
l-156-'572 


1-1680649 


1-1806831 


1-1939446 


1-2078794 


1-2225202 


53 




1-1682701 


1-1808988 


1-1941712 


1-2081175 


1-2227703 


52 




1-1564525 


1-1684755 


1-1811140 


1-1943980 


1-2083559 


1-2230207 


51 




11560480 


1-1086810 


1-1813307 


1-1946251 


1-2085944 


1-2232713 


50 




11568436 


1-1688867 


11815469 


1-1948523 


1-2088331 


1-2235222 


49 




1-1570394 


1-1690926 


1-1817633 


1-1950796 


1-2090720 


1-2-237732 


48 




1-1572354 


1-1692986 


1-1819798 


1-1953072 


1-2093112 


1-2240244 


47 




11574315 


1-1695048 


1-1821966 


1-1955350 


1-2095505 


1-2242758 


46 




1-1576278 


1-1697112 


1-1824135 


1-1957629 


1-2097900 


1-2245274 


45 




1-1578243 


1-1699178 


1-1826306 


1-1959911 


1-21 00-297 


1-2247793 


44 




1-1580209 


1-1701245 


1-1828479 


1-1962194 


1-2102696 


1-2250313 


43 




1-158-J177 


1-1703314 


1-1830654 


1-1964479 


1-2105097 


1-2252836 


42 




1-1584146 


1-1705385 


1-1832830 


1-1966767 


1-2107500 


1-2-255361 


41 


20 


1-1586118 


11707457 


1-1835008 


1-1969056 


1-2109905 


1-2257887 


40 


SI 


1-1588091 


1-1709531 


1-1837188 


1-1971346 


1-2112312 


1-2260416 


39 


22 


1-1590065 


1-1711607 


1-1839370 


1-1973639 


1-2114721 


1 •2-262947 


38 


23 


1-1592041 


1-1713685 


1-1841554 


1-1975934 


1-2117132 


1-2265480 


37 


Ik 


1-1591019 


1-1715764 


1-1843739 


1-1978230 


1-2119545 


1-2268015 


36 


25 


1-1595999 


1-1717845 


1-1845927 


1-1980529 


1-2121960 


1-2270552 


35 


S6 


1-1597980 


1-1719928 


1-1848116 


1-1982829 


1-2124377 


1-2273091 


34 


27 


1-1599963 


1-1722013 


1-1850307 


1-1985131 


1-2126795 


1-2275633 


33 


28 


1-1601947 


1-1724099 


1-1852500 


1-1987435 


1-2129216 


1-2-278176 


32 


2» 


1-1603933 


1-1726187 


1-1854694 


1-1989741 


1-2131639 


1-2280722 


31 


80 


1-1605921 


1-1728277 


1-1856890 


1-1992049 


1-2134064 


1-2283269 


30 


31 


1-1007911 


1-1730368 


1-1859089 


1-1994359 


1-2136191 


1-2285819 


29 


32 


1-1609902 


11732462 


1-1861289 


1-1996671 


1-2138920 


1-2288371 


28 


33 


1-1611894 


1-1734557 


1-1863490 


1-1998-85 


1-2141351 


1-2290924 


27 


34 


1-1613889 


1-173G653 


1-1865694 


1-2001300 


1-2143784 


1-2293480 


26 


35 


11615885 


1-1738752 


1-1867900 


1-2003618 


1-2146218 


1-2296039 


25 


36 


1 161 7883 


1-1740852 


1-1870107 


1-2005937 


1-2148655 


1-2298599 


24 


37 


1-1619882 


1-1742954 


1-1872316 


1-2008258 


1-2151094 


1-2301161 


23 


38 


1-1621883 


1-1745058 


1-1874527 


1-2010582 


1-2153535 


1-2303725 


22 


39 


1-1623886 


1-1747163 


1-1876740 


1-201-2907 


1-2155978 


1-2306292 


21 


40 


1-1625891 


1-1749270 


1-1878954 


1-2015234 


1-2158423 


1-2308861 


20 


41 


1-1627897 


1-1751379 


1-1881171 


1-2017563 


1-2160870 


1-2311432 


19 


43 


1-1629905 


1-1753490 


1-1883389 


1-2019894 


1-2163319 


1-2314004 


18 


43 


1-1631914 


1-1755603 


l-lb85609 


1-2022226 


1-2165770 


1-2316579 


17 


41 


1-1633925 


1-1757717 


118b7831 


1-2024561 


1-21682-23 


1-2319156 


16 


43 


1-1635938 


1-1759833 


1-1890055 


1-2020898 


. 1-2170678 


1-2321736 


15 


4ff 


1-1637953 


1-1761951 


1-1892280 


1-2029236 


1-2173135 


1-2324317 


14 


47 


1-1639969 


1-1764070 


1-1894508 


1-2031577 


1-2175594 


l-2326rO0 


13 


48 


1-1641987 


1-1766191 


1-1896737 


1-2033919 


1-2178055 


1-2329486 


12 


49 


1 1644007 


1-1768314 


1-1898968 


1-2036264 


1-2180518 


1-2332074 


H 


50 


1^646028 


1-1770439 


1-1901201 


1-2038610 


1-2182983 


1-2334664 


10 


51 


1-1648051 


1-1772566 


1-1903436 


1-2040958 


1-2185450 


1-2337256 


9 


58 


1-1650076 


1-1774694 


1-1905673 


1-2043308 


1-2187919 


1-2339H50 


8 


53 


1-1652102 


1-1776824 


lly079U 


1-2045660 


1-2190390 


1-2342446 


7 


64 


1-1654130 


1-1778956 


1-1910152 


1-2048014 


1-2192864 


r2345044 





55 


1-1656160 


1-1781069 


1-1912394 


1-2050370 


1-2195339 


1-2347645 


9 


56 


11658191 


1-17«3225 


1-1914638 


1-2052728 


1-2197816 


1-2350248 


4 


57 


1-1660-2-J4 


1-I7653(i2 


1-1916884 


1-2055088 


l-2-.'00-i96 


1-2352852 


3 


56 


1-1662259 


1-1787501 


1-I91yl32 


1-2057450 


1 •2-20-2777 


1-2355459 


S 


SO 


1-1664290 


1-1789(J42 


11!)213^1 


1-2069814 


1 '2-205260 


1 -2358069 


1 


(iO 


1-1666334 


l-17'Jl7d4 


1-1923633 


1-2062179 


1-2207746 


1 •2360680 





/ 


t^r 


W 


hV 


66" 


65'^ 


?*' 


/ 


U 






Cosecants. 







478 



SECANTS AND COSECANTS. 



Secajtts. 



41 
43 
43 

44 
45 

46 
47 
48 
49 
60 

61 
63 
53 
64 
65 

66 
67 



36' 


37** 


38'' 


39^ 


40° 


41° 


1-2360680 


1-2521357 


1-2690182 


1-2867596 


1-3054073 


1-3250130 


1-2363293 


1-2524102 


1-2693067 


1-2870628 


1-3057261 


1-325348^ 


1-2363909 


1-2526850 


1-2695955 


1-2873663 


1-3060451 


1-3256837 


1-2368526 


1-2529601 


1-2698845 


1-2876700 


1-3063644 


1-3260194 


1-2371146 


1-2532353 


1-2701737 


1-2879710 


1-3066839 


1-3-263554 


1 ■2373768 


1-2535108 


1-2704632 


1-2882782 


1-3070038 


1-326G918 


1-2376393 


1-2537865 


1-2707529 


1-28858-27 


1-3073239 


1 -3270284 


1-3379019 


1-2540625 


1-2710129 


1-2888875 


1-3076443 


1-3273653 


1-2381647 


1-2543387 


1-2713331 


1-2891925 


1-3079649 


1-3277024 


1-2384278 


1-2516151 


1-2716235 


1-2891977 


1-3082858 


1-3280399 


1-2386911 


1-2548917 


1-2719142 


1-2898032 


1-3086069 


1-3283776 


1-2389546 


1-2551685 


1-27-22052 


1-2901090 


1-3089284 


1-3287156 


1-2392183 


1-2554456 


1-2721963 


1-2904150 


1-3092501 


1-S290539 


1-2394823 


1-25572-J3 


1-2727877 


1-2907213 


1-3095720 


1-3293925 


1-2397464 


1-2560005 


1-2730794 


1-2910278 


1-3098943 


1-3297314 


1-2400108 


1-256-2782 


1-2733712 


1-2913316 


1-3102168 


1-3300706 


1 2402764 


1-2565562 


1-2736634 


1-2916416 


1-3105396 


1-3304100 


1-2105402 


1 -2568345 


1-2739557 


1-2919189 


1-3108626 


1-3307197 


1-2108053 


1-2571129 


1-271^184 


1-2922564 


1-3111860 


J -3310897 


1-2110704 


1-2572916 


1-2745112 


1-2925642 


1-3115095 


1-3314301 


1-2413359 


1-2576705 


1-2718313 


1-2928723 


1-3118334 


1-3317707 


1-211C016 


1-2579497 


1-2751276 


1-2931806 


1-3121575 


1-3321115 


1-2U8675 


1-2582291 


1-2751212 


1-2931892 


1-3124820 


1-3324527 


1-2121336 


1-2585087 


1-2757151 


1-2937980 


1-3128066 


1 •33-27912 


1-2423999 


1-2587885 


1-2760091 


1-2941071 


1-3131316 


1-3331359 
1-3334779 


1 -2426665 


1 -2590083 


1-2763034 


1-2944164 


1-3134568 


1-2429333 


1-25931&D 


1-2765980 


1-2947260 


1-3137823 


1-3338203 


1-2432003 


1-2596294 


1 276^^28 


1-2950359 


1-3141081 


1-3^1029 


1-2184675 


1-2599103 


1-2771878 


I-:i953160 


1-3144341 


1-3315058 


1-2437349 


1-2601912 


1-2771831 


1-2956564 


1-3147604 


1-3318189 


1-2440026 


1-2604724 


1-2777787 


1-2959670 


1-3150870 


1-3351924 


1-2442704 


1-2607539 


1-2780744 


1-2962779 


1-3154139 


1-3355362 


1-2415385 


1-2610356 


1-2783705 


1-2965890 


1-3157410 


1-3358802 


1-2448069 


1-2613175 


1 -2786667 


I-296D004 


1-3160C84 


1-336-2-246 


1-2450754 


1-2615997 


1-2789632 


1-2972121 


1-3163961 


1-3365692 


1-2453442 


1 -2618820 


1-2792600 


1-2975-240 


1-3167240 


1-3369141 


1-2456131 


1-2621617 


1-2790570 


1-2978362 


1-3170523 


1-3372594 


1-24588-23 


1-2621175 


1 -2798543 


1-29S11S7 


1-3173808 


1-8376049 


1-2461518 


1-26-27306 


1-2«01518 


1-2981614 


1-3177096 


1-3379507 


1 "2164214 


1-2630 no 


1-2801195 


1-^987713 


1-3180380 


1-6382968 


1-2466913 


1-2632975 


1-2807475 


1-2990876 


1-3183680 


13386432 


1-24696U 


1-2635813 


1-2810157 


1-^991011 


1-3186976 


1-3389898 


1 -247-2317 


l-263b653 


1-2813142 


1 -21^0 7 118 


1-3190274 


1-3393368 


1-2475022 


1-2611198 


1-2816130 


1-3000288 


1-3193576 


1-3396841 


1-2477730 


1-2611311 


1-2819119 


1-3003131 


1-3196881 


1-3100316 


1 -2180440 


l-20471fci8 


1-2822112 


1-3006576 


1-3200188 


1-3103795 


1-2483152 


1-2650038 


l-2c?25407 


1-3009724 


1-3203498 


1-3407276 


1-2485866 


1-2652890 


1-2828404 


1-301-2875 


1-3206810 


1-3410761 


1-2488583 


1-2655715 


1-2831404 


1-3016028 


1-3210126 


1-3414-248 


1-2191302 


1-2658G01 


1-2834106 


1-3019184 


1-3213444 


1-3417738 


1 •24940^3 


1-2661460 


1-2837411 


1-302-2313 


1-3216705 


1-3421232 


1-2196746 


1-2664328 


1-2810418 


1-3025504 


1-3220089 


1-3424728 


1-2499171 


1-2667186 


1-2813423 


1-3028667 


1-3223116 


1-3428-227 


1-2602199 


1-2670052 


1-2816140 


1-3031834 


1-3226745 


1 3131729 


1-2501929 


1 -2672921 


1-2819155 


1-3035003 


1-3230078 


1-3135234 


1-2507661 


1-2675792 


1-2852472 


1-3038175 


1-3233413 


1-3138742 


1-2510396 


1-2678665 


1-2855192 


1-3041349 


1-3236750 


1-344225S 


1-2513133 


1-2681511 


1-2858514 


1-3044526 


1-3240091 


1-3140767 


1-2516872 


1-2681419 


1-2861539 


1-3017706 


1-3213135 


1-3149284 


1-2518618 


1-2687-299 


1-2864566 


1-3050883 


1-3216781 


1-3152804 


1 •2521307 


1 •26901-32 


1-2867598 


1-3054073 


1-8250130 


1-3456327 


63^ 


62'* 


61° 


50° 


49° 


4S° 



Cosecants. 



SECANTS AND COSECANTS. 



479 



/ 






Secants. 






# 


42' 


43'' 


44' 


45' 


46' 


47' 





1- 


J45C327 


1-3673275 


1-3901636 


1-4142136 


1-4395555 


1-4662792 


60 


1 


1- 


J459853 


1-3676985 


1-3903543 


1-4146-251 


1-4399904 


1-4667368 


59 


2 


1- 


J463382 


1-3680699 


1-3909453 


1-4150370 


1^4404246 


1-4671948 


58 


3 


1- 


»(J6914 


1-3684416 


1-3913366 


1-4154493 


1-4408592 


1 •4676532 


67 


4 


1- 


J470449 


1-3688136 


1-3917-283 


1-4158619 


14412941 


1-4681120 


56 


5 


1- 


3473987 


1-3691859 


1-3921203 


1-4162749 


1-4417295 


1-4685713 


55 


6 


1 


3477528 


1-3695586 


1-3925127 


1-4166883 


1-4421652 


1-4690309 


54 


7 


1 


3481072 


1-3699315 


1-3929054 


1-41710-20 


1-4426013 


1-4694910 


53 


8 


1- 


3484619 


1-3703048 


1-3932985 


1-4175161 


1-4430379 


1 -4699514 


52 


9 


1- 


3488168 


1-3706784 


1-3936918 


1-417930G 


1-4434748 


1^4704123 


51 


10 


1- 


3491721 


1-3710523 


1-3940856 


1-4183454 


1-4439120 


1^4708736 


50 


11 


1- 


3495277 


1-3714266 


1-3914796 


1-4187605 


1-4443497 


1 •4713354 


49 


12 


1- 


3498836 


1-3718011 


1-3948740 


1-4191761 


1-4447878 


1 •4717975 


48 


13 


r 


3502398 


1 •37-21 760 


1-395-2688 


1-4195920 


1-4452263 


1^4722600 


47 


U 


1 


3505963 


1-3725512 


1-3956639 


l-4-?0008-3 


1-4456651 


1^4727230 


46 


15 


1- 


3509531 


1-3729268 


1-3960593 


1-4204248 


1-4461043 


1^4731864 


45 


16 


1- 


3513102 


1-3733026 


1-3964551 


1-4208418 


1-4465439 


1-4736502 


44 


17 


1- 


3516677 


1-3736788 


1-3968512 


1-4212592 


1-44G9839 


1-4741144 


43 


18 


1 


3520254 


1-3740553 


K3972477 


1-4216769 


1-4474243 


1-4745790 


42 


19 


1 


3523834 


1-3744321 


1-3976445 


1-4220950 


1-4478651 


1-4750440 


41 


20 


1- 


3527417 


1-3748092 


1-3980416 


1-4225134 


1-4483063 


1-4755095 


40 


21 


1 


3531003 


1-3751867 


1-3984391 


1-4229323 


1-4487478 


1-4759754 


39 


22 


1 


3534593 


1-3755645 


1-3988369 


1-4233514 


1-4491898 


1-4764417 


38 


23 


1- 


3538185 


1-3759426 


1 •399-2351 


1-4237710 


1-44963-22 


1-4769084 


37 


2i 


1- 


3541780 


1-3763210 


1 •3996336 


1-4241909 


1-4500749 


1-4773755 


36 


25 


1- 


3545379 


1-3766998 


1 •40003-25 


1-4246112 


1-4505181 


1-4778431 


35 


26 


r 


3548980 


1-3770789 


1-4004317 


14250319 


1-4509616 


1-4788111 


34 


27 


1- 


3552585 


1-3774583 


i '4008313 


1425 45-29 


1-4514055 


1-4787795 


33 


28 


1 


3556193 


1-3778380 


1-4012312 


1-4258743 


1-4518498 


1-4792483 


32 


29 


1 


3559803 


1-3782181 


1-4016315 


1-4262961 


1-4522946 


1-4797176 


31 


30 


1 


3563417 


1-3785985 


1-4020321 


1 •4267182 


1-4527397 


1-4801872 


30 


31 


1 


3567034 


1-3789792 


1-4024330 


1-4271407 


1-4531852 


1-4806573 


29 


32 


1 


3570654 


1-3793602 


1-4028343 


1-4275636 


1-4536311 


1-4811278 


28 


32 


1 


3574277 


1-3797416 


1-4032360 


1-4279868 


1-4540774 


1-4815988 


27 


34 


1 


3577903 


1-3801233 


1-4036380 


1-4284105 


1-4545241 


1-4820702 


26 


35 


1 


3581532 


1-3805053 


1-4040403 


1-4288345 


1-4549712 


1-4825420 


25 


36 


1 


3585164 


1-3808877 


1-4044430 


1-4292588 


1-4554187 


1-4830142 


24 


37 


1 


3588800 


1-3812704 


1-4048461 


1-4296836 


1-4558666 


1-4834868 


23 


38 


1 


3592438 


1-3816534 


1-4052494 


1-4301087 


1-4563149 


1-4839599 


22 


39 


1 


•3596080 


1-3820367 


1-4056532 


1-4305342 


1-4567636 


1-4844334 


21 


40 


1 


•3599725 


1-3824204 


1-4060573 


1-4309600 


1-4572127 


1-4849073 


20 


41 


1 


•3603372 


1-3828044 


1-4064617 


1-4313863 


1-4576621 


1-4853817 


19 


42 


1 


•3607023 


1-3831887 


1-4068665 


14318129 


1-4581120 


1-4858565 


18 


43 


1 


•3610677 


1-3835734 


1-4072717 


1-4322399 


1-4585623 


1-4863317 


17 


44 


1 


-3614334 


1-38395^4 


1-4076772 


1-4326672 


1-4590130 


1-4S68073 


16 


d5 


1 


•3617995 


1-3843437 


1-4080831 


1-4330950 


1-4594641 


1-4872834 


15 


46 


1 


•3621658 


1-3847294 


1-4084893 


1-4335231 


1-4599156 


1-4877599 


14 


47 


1 


•3625324 


1-3851153 


1-4088958 


1-4339516 


1-4603675 


1-4882369 


13 


48 


1 


•3628994 


1-3855017 


1-4093028 


1-4343805 


1-4608198 


1-4887142 


li 


49 


1 


•3632667 


1-3858883 


1-4097100 


1-4348097 


1-4612726 


1-4891920 


11 


SO 


1 


•3636343 


1-3862753 


14101177 


1-4352393 


1-4617257 


1-4896703 


10 


51 


1 


•3640022 


1-3866626 


1.-4105257 


1-4356693 


1-4621792 


1-4901489 


9 


52 


1 


•3643704 


1-3870503 


1-4109340 


1-4360997 


1-4626331 


1-4906280 


8 


53 


1 


•3647389 


1-3874383 


1-4113427 


1-4365305 


1-4630875 


1-4911076 


7 


54 


1 


•3651078 


1-3878266 


1-4117517 


1-436961G 


r4635422 


1-49 1 5875 


6 


55 


1 


•3654770 


1^3882153 


1-4121612 


1-4373932 


1-4639973 


1-4920680 


5 


56 


] 


•3658464 


1^3886043 


1-4125709 


1-4378251 


1 •4644529 


1-4925488 


4 


57 


1 


•3662162 


1^38S9935 


1-4129810 


1-4382574 


1 •4649089 


1-4930301 


3 


68 


1 


•3665863 


1 •3893832 


1-4133915 


1-4386900 


1-4653652 


1-4935118 


8 


59 


1 


•3669567 


1-3897733 


1-4138024 


1-4391231 


r4658220 


1-4'j39940 


1 


60 


1-3673275 


1-3901636 


1-4142136 


1-4390565 


1-4662792 


1-4944765 





/ 


47- 


46' 


46' 


44' 


43' 


42' 


/ 




. 


Cosecants. 







480 



SECANTS AND COSECANTS. 



^ 






Secants. 






t 




49^ 


50^ 


5r 


52^ 


53' 





1 -4944765 


1 


•5242531 


1-5557238 


1-5890157 


1-6242692 


1-6616401 


60 


1 


1-49 J 9096 


1 


-5247634 


1-5562634 


1 -5895868 


1-6248743 


1-6622819 


59 


2 


1-4954431 


1 


-5252741 


1-5568035 


1-5901584 


1-6254799 


1-6629243 


58 


3 


1-4059270 


1 


-5257854 


1-5573441 


1-5907306 


1-6-260861 


1-6635673 


57 


4 


11964113 


1 


•5262971 


r5578852 


1-5913033 


1-6-266929 


1-6642110 


56 


5 


1-49G8961 


1 


•5268093 


1-5584268 


1-5918766 


1 •6-273003 


1-6648553 


65 


6 


1-4973813 


1 


•5273219 


1 •5589689 


1-5924504 


1-6279083 


1-6655002 


54 


7 


l-4978o70 


1 


•5278351 


1-5595115 


1-5930247 


1^6285169 


1-6661458 


53 


8 


1 -4953531 


1 


•5283487 


1-5500546 


1-5935996 


1-6-29 1-261 


1 •6667920 


52 


9 


1-49S8337 


1 


•5288627 


1-5605982 


i-5941751 


1-6297359 


1-6674389 


51 


10 


1-4993267 


1 


•5293773 


1-5611424 


1-5947511 


1-6303462 


1-6680864 


50 


11 


J-4998141 


1 


5298923 


1-5616871 


1-5953276 


1 •6309572 


16687345 


49 


12 


1-5003020 


1 


•5304078 


1-56-223-22 


1-5959043 


16315688 


1-6693833 


48 


13 


1-5007903 


1 


•5309233 


1-56-27779 


1-5964824 


1-6321809 


1-6700328 


47 


14 


1-5012791 


1 


•5314403 


1-5633-241 


1-5970606 


1^6327937 


1-6706828 


46 


15 


1-5017G83 


1 


5319572 


1-5638708 


1-5976394 


1 •6334070 


1-6713336 


45 


16 


1 •50-22580 


1 


•5324746 


1-5644181 


1-5982187 


1-6340210 


1-6719850 


44 


17 


1 -5027481 


1 


-5329925 


1-5649658 


1-5987986 


1 •6346355 


1^6726370 


43 


18 


1-5032387 


1 


5335109 


1-5655141 


1-5993790 


1-6352507 


1 •673-2897 


42 


19 


1-5037:297 


1 


•5340297 


1-56606-28 


1-5999600 


1-6358664 


1 •6739430 


41 


20 


1-5042211 


1 


5345491 


1-5666121 


1-6005416 


1-6364828 


1^6745970 


40 


21 


1-5047131 


1 


5350689 


1-5671619 


1-6011237 


1-6370997 


1-6752517 


39 


22 


1-5052054 


1 


5355892 


1-5677123 


1-6017064 


1-6377173 


1-6759070 


38 


23 


l-505{)982 


1 


5361100 


1-5682631 


1-6022896 
1-6028734 


1-6383355 


1-6765629 


37 


24 


1-5061915 


1 


5366313 


1-5688145 


1-6389542 


1-6772195 


36 


25 


1-506GS5!? 


1 


5371530 


1-5693664 


1-6034577 


1-6395736 


1-6778768 


35 


26 


1-5071793 


1 


5376752 


1-5699188 


1-6040426 


1-6401936 


1-6785347 


34 


27 


1-507C739 


1 


5381980 


1-5704717 


1-6046281 


1-6408142 


1-6791933 


33 


28 


1-508IG90 


1 


5387212 


1-5710252 


16052142 


1-6414354 


1-6798525 


32 


29 


1-5086045 


1 


5392449 


1-5715792 


1-6058008 


1-6420572 


16805124 


31 


30 


1-5091305 


1- 


5397690 


1-5721337 


1-6063879 


1-6426796 


1^6811730 


30 


31 


1-5096569 


1 


5402937 


1-5726887 


1-6069757 


1-6433027 


1 •6818342 


29 


32 


1-^101538 


1- 


5408189 


1-5732443 


1-6075640 


1-6439263 


1-6824961 


28 


33 


1-5106511 


1 


5413445 


1-5738004 


1-60815-28 


1^6445506 


1-6831586 


27 


34 


1-5111489 


1- 


5418706 


1-5743570 


1-6087423 


1-6451754 


1-6838219 


26 


35 


1-5116472 


1 


5423973 


1-5749141 


1-6093323 


1-6458009 


1-6844857 


25 


36 


1-5121459 


1 


5429244 


1-5754718 


1-6099228 


1-6464270 


1-6851503 


24 


37 


1-5126150 


1 


54345-20 


1-5760300 


1-6105140 


1-6470537 


1 •6858155 


23 


38 


1-5131446 


1- 


5439801 


1-5765887 


1-6111057 


1-6476811 


1-6864814 


23 


39 


1-5136447 


1 


5445087 


1-5771479 


1-6116980 


1-6483090 


1-6871479 


21 


40 


1-5141452 


1- 


5450378 


15777077 


1-6122908 


1-6489376 


1-6878151 


20 


41 


1-5146462 


1- 


5455673 


1-578-2680 


1-6128843 


1-6495668 


1-6884830 


19 


42 


1-5151477 


1- 


5460974 


1 -5783-289 


1-6134783 


1-6501966 


1-6891516 


18 


43 


1-5156496 


1 


5466280 


1-5793902 


1-6140728 


1-6508270 


1-6898208 


17 


44 


1-5161520 


1- 


5471590 


1-5799521 


1-6146680 


1-6514581 


1-6904907 


16 


45 


1-5166548 


1- 


5476906 


1-5S05146 


1-6152637 


1-6520898 


1-6911613 


15 


46 


1-5171581 


1- 


548-2226 


1-5810776 


1-6158600 


1-6527221 


1-6918326 


14 


47 


1-5176619 


1- 


5487552 


1-5816411 


1-6164569 


1-6533550 


1-6925045 


13 


48 


1-5181661 


1- 


5492882 


1-58-2-2051 


1-6170544 


1-6539885 


1-6931771 


12 


49 


1-5186708 


1 


5498218 


1-5827697 


1-6176524 


1-6546227 


1-6938504 


11 


50 


1-5191759 


1 


5503558 


1-5833348 


1-618-2510 


1-6552575 


1-6945244 


10 


51 


1-5196815 


1 


5508904 


1-5839005 


1-6188502 


1-6558929 


1 •6951990 


9 


62 


1-5201876 


1 


5514254 


1-5844667 


1-6194500 


1-6565290 


1 •6958744 


8 


53 


l'5i'06942 


1- 


5519610 


1-5850334 


1-6-200504 


1-6571657 


1-6965504 


7 


54 


1-5212012 


1 


5524970 


1-5S56007 


1-6206513 


1-6578030 


1-6972271 


6 


55 


1-5217087 


1- 


5530335 


1-5861,685 


1-6212523 


1-6584409 


1-6979044 


6 


56 


1-5222166 


1- 


5535706 


1 -5867369 


1-6218549 


1-6590795 


1-6985825 


i 


57 


1-5227250 


1- 


5541081 


1-5873058 


1-62-24576 


1-6597187 


1-6992612 


8 


58 


1 •5232339 


1- 


5546462 


1-5878752 


1-6230609 


1-6603586 


1-6999407 


8 


59 


1-5237433 


r 


5551848 


1-5884452 


1-6236648 


1 •6609990 


1-7006208 


1 


€0 


1-5242531 


1-6557238 


1-5890157 


1-6242692 


1-6616401 


1-7013016 





/ 


41' 


40'' 


zr 


38» 


37' 


86« 


/ 






Cosecants. 







SECAKTS AKT) COSECANTS. 



481 



Secants. 



21 
25 

26 
27 
28 
29 
: 30 

31 
32 
33 
34 
35 

36 
37 



41 
42 
43 
44 
45 

46 
47 

48 
49 
SO 

51 
52 
53 
54 
55 

56 
67 



54" 


55** 


56"* 


57** 


58** 


5r 


1-7013016 


1-7431468 


1-7882916 


1-8360785 


1-8870799 


1-9416010 


1-7019831 


1-7441715 


1-7890633 


1-8369013 


1-8879589 


1-9425445 


1-7026653 


1-7418969 


1-7898357 


1-8377251 


1-8888388 


1-94348G1 


1-7033482 


1-7456230 


1-790C090 


1-8383198 


1-8897197 


1-9444288 


1-7040318 


1-7463499 


1-7913831 


1-8393753 


1-8906016 


1-9453725 


1T047169 


1-7470776 


1-7921580 


1-8102013 


1-8914845 


1-9463173 


1-7054010 


1-7478060 


1-7929337 


1-8110292 


1-8923681 


1-9472632 


1-7060867 


1-7485352 


1-7937102 


1-8118571 


1-8932532 


1-9482102 


1-7067730 


1-7492651 


1-7944876 


1-8426866 


1-8941391 


19491583 


1-7074601 


1-7199958 


1-7952658 


1-8435166 


1-8950-259 


1-9501075 


1-7081478 


1-7507273 


1-7960419 


1-8443476 


1-8959138 


1-9510577 


1-7088362 


1-7514595 


1-7968247 


1-8451795 


1-8968026 


1-9520091 


1-7095254 


1-7521921 


1-7976054 


1-8460123 


1-8976921 


1-95-29615 


1-7102152 


1-7529262 


1-7983869 


1-8468460 


1-8985832 


1-9539150 


1-7109038 


1-7536607 


1-7991693 


1-8176806 


1-8994750 


1-9548697 


1-7115970 


1-7543959 


1-7999524 


1-8485161 


1-9003678 


1-9558251 


1-7122890 


1-7551320 


1-8007365 


1-8193525 


1-9012616 


1-9567822 


1-7129817 


1 -75:18687 


1-8015213 


1-8501898 


1-90-21564 


1-9577402 


1-7136750 


1-7566063 


1-8023070 


1-8510281 


1-9030522 


1-9586992 


] -7143691 


1-7573416 


1-8030935 


1-8518672 


1-9039491 


1-9596593 


1-7150639 


1-7580837 


1-8038809 


1-8527073 


1-9018469 


1-9606206 


1-7157594 


1-7588236 


1-801G691 


1-8535483 


1-9057457 


1-9615829 


1-7164556 


1-7595642 


l-805i582 


1-8543903 


1-9066156 


1-9625464 


1-7171525 


1-7603057 


1 -8062181 


1-8552331 


1-9075461 


1-9635110 


1-7178501 


1-7610478 


1-8070388 


1-8560769 


1-9084483 


1-9644767 


1-7185184 


; 1-7617908 


1-8078304 


1-8569216 


1-9093512 


1-9654435 


1-7192475 


1-7625345 


1-8086228 


1-8577672 


1-910-2551 


1-96641U 


1-7199172 


1-7632791 


1-8091161 


1-8586138 


1-9111600 


1-9673805 


1-7-206477 


1-7640241 


1-8102102 


1-8594612 


1-9120659 


1-9683507 


1-7213489 


1-7647704 


1-8110052 


1-8603097 


1-9129729 


1-9693220 


1-7220508 


1-7655173 


1-8118010 


1-8611590 


1-91 38809 


1-9702911 


1-7227534 


1 -76626 19 


1-8125977 


1-8620093 


1-9147899 


1-9712680 


1-7234568 


1-7670133 


1-8133953 


1-86-28605 


1-915G999 


1-9722427 


1-7241609 


1-76776-25 


1-8U1937 


1-8637126 


1-91G6110 


1-9732185 


1-7248657 


1-7685125 


1-81499-29 


1-8645657 


1-9175230 


1-9741951 


1-7235712 


1-7692633 


1-8157930 


1-8G54197 


1-9184362 


1-9751735 


1-7262774 


1-7700149 


1-8165940 


1-8662717 


1-9193503 


1*9761527 


1-7269841 


1-7707672 


1-8173958 


1-8671306 


1-9-202655 


1-9771331 


1-7276921 


1-7715204 


1-8181985 


1-8679875 


1-9211817 


1-9781146 


1-7284005 


1-7722743 


1-8190021 


1-8688453 


1-9220990 


1-9790972 


1-7291096 


1-7730-29O 


1-8198065 


1-8699010 


1-9230173 


1-9800810 


1-7298195 


1-7737815 


1-8206118 


1-8705637 


1-9239366 


1-9810659 


1-7305301 


1-7745409 


1-8211179 


1-8714244 


1-9248570 


1 -98205-^0 


l-73r24U 


1-7752980 


1-8-22-J-219 


1-87-22859 


1-9257784 


1-9830393 


1-7319535 


1-7760559 


1-8230328 


1-8731485 


1-9267009 


1-9840276 


1-7S2668S 


1-7768116 


1-8238116 


1-8710120 


1-9276244 


1-9850172 


1-7333798 


' 1-7775711 


1-8216512 


1-8748761 


1 -9285400 


1-9860080 


1-7340911 


1-7783314 


1-8254017 


1-8757419 


1-9294746 


1-9869997 


1-7348091 


1-7790955 


1-8362731 


1-8766082 


1-9304013 


1-9879927 


1-7355248 


1-7798571 


1-8270851 


1-8774755 


1-9313290 


1-9889869 


1-7362413 


1-7806201 


1-8278985 


1-8783438 


1-9322578 


1-9899822 


1-7369585 


1-781383G 


1-8287125 


1-8792131 


1-9331876 


1-9909787 


1-7376764 


1-7821179 


1-8295271 


1-8800833 


1-9341185 


1-9919764 


1-7383951 


1-7829131 


1-8303432 


1-8809545 


1-9350305 


1-9929752 


1-7391145 


1-7836790 


1-8311599 


1-8818266 


1-9359835 


1-9939753 


1-7398317 


1-7811157 


1-8319771 


1-8826998 


1-9369175 


•1-9949764 


1-7405556 


1-7852133 


1-8327959 


1-8835738 


1-9378527 


1-9959783 


1-7112773 


1-7859817 


1-8336152 


1-8844489 


1-9387889 


1-99G9823 


1-7419997 


1-7867508 


1-8314354 


1 •8858-219 


1-9397:^62 


1-9979870 


1-7127229 


1-7875-208 


1-8352565 


1-8862019 


1-940G646 


1-99899-29 


1-7431168 


1-7882916 


1-8360785 


1-8870799 


1-9416010 


20000000 


''^ 


34» 


sa** 


32* 


31'' 


30" 



Cosecants. 



1 



482 




SECAKTS AND 


COftT:nA>TTS. 






t 






Secants. 






1 


60' 


6r 


62* 


63* 


64^* 


65^ 



1 


S-&OO0OOO 


2 -0626653 


2*1300545 


2-2026893 


2-2811720 


2-3662016 


60 

59 
58 
57 
56 
55 


•' V-0010083 


2-0037484 


2-1312-205 


2-2039476 


2-2825335 


2-3676787 


2 


^.0020177 


2-06483-28 


2-1323830 


2-2052075 


2-2838967 


2-3691578 


3 


2-0030281 


20659186 


2-1335570 


2-2064691 


2-2852618 


2-3706390 


4 


20010402 


2-0670056 


2-1347274 


2-2077323 


2-2866286 


2-3721222 


5 


2 0050532 


2-0680940 


2-1358993 


2-2089972 


2-2879974 


2-3736075 


6 


2-0060674 


2-0691836 


2-1370726 


2-2102637 


2-2893679 


2-3750949 


54 
53 
52 


7 


2-00708-28 


2-0702746 


2-1382475 


2-2115318 


2-2907403 


2-3765843 


8 


2-0080994 


2-0713670 


2-1394238 


2-2128016 


2-2921145 


2-3780758 


51 

50 


9 


2-0091172 


2-0724606 


2-1406015 


2-2140730 


2-2934906 


2-3795694 


10 


20101362 


2-0735556 


2-1417808 


2-2153460 


2-2948685 


2-3810650 


11 


2-0111564 


2-0746519 


2-1429615 


2-2166208 


2-2962483 


2-3825627 


49 
48 
47 
46 
45 


12 


20121779 


2-r757496 


2-1441438 


2-2178971 


2-2976299 


2-3840625 


13 


2-0132005 


2-0768486 


2-1453-275 


2-2191752 


2-2990134 


2-3855645 


H 


2-0142243 


2-0779489 


2-1465127 


2-2204548 


2-3003988 


2-3870685 


15 


2-0152494 


2-0790506 


2-1476993 


2-2217362 


2-3017860 


2-3885746 


16 


2-01 6-2756 


20801536 


2-1488875 


2-2230192 


2-3031751 


2-3900828 


44 

43- 
42 
41 

40 


17 


2-0173031 


2-0812580 


2-1500772 


2-?243039 


2-3045660 


2-3915931 


18 


2-0183318 


2-0823637 


2-1512684 


2-1255903 


2-3059588 


2-3931055 


19 


20193618 


2-0834708 


2-1524611 


2-2268783 


2-3073536 


2-3946201 


SO 


2-0203929 


2-0845792 


2-1536553 


2-2281681 


2-3087501 


2-3961367 


21 


2-0214253 


2-0856890 


2-1548510 


2-2294595 


2-3101486 


2-3976555 


39 
38 
37 
36 
35 


22 


2-0224589 


2-0868002 


2-1560482 


2-2307526 


2-3115490 


2-3991764 


23 


2-0234937 


2-0879127 


2-1572469 


2-2320474 


2-3129513 


2-4006995 


24 


2-0245297 


2-0890265 


2-1584471 


2-2333438 


2-3143554 


2-402-2247 


25 


2-0255670 


2-0901418 


2-1596489 


2-2346420 


2-3157615 


2-4037520 


26 


2-0266056 


2-0912584 


2-1608522 


2-2359419 


2-3171695 


2-4052815 


34 
33 
32 
31 • 
30. 


27 


2-0276453 


2-0923764 


2-1620570 


2-2372435 


2-3185794 


2-4068132 


28 


2-0286863 


20934957 


21632633 


2-2385468 


2-3199912 


2-4083469 


29 


2-0297286 


2-0946164 


2-1644712 


2-2398517 


2-3214049 


2-4098829 


30 


20307720 


2-0957385 


2-1656806 


2-2411585 


2-32-28205 


2-4114210 


31 
32 


2-0318168 


2-0968620 


2-1668915 


■2-2424669 


2-3242381 


2-4129613 


S9 

28 
27 
26 
25 


2-0328628 


2-0979869 


2-1681040 


2-2437770 


2- 3-356575 


2-4145038 


33 
34 
35 


20339100 


2-0991131 


2-1693180 


2-2450889 


2-3270790 


2-4160484 


10349585 


21002408 


2-1705335 


2-2464025 


2-3285023 


2-4175952 


2-0360082 


2-1013698 


2-1717506 


2-2477178 


2-3299276 


2-4191442 


36 


2-0370592 


2-1025002 


2-1729693 


2-2490348 


2-331S548 


2-4206954 


24 
23 
'22 
21 
20 


37 


2-0381114 


2-1036320 


2-1741895 


2-2503536 


2-3327840 


2-422-2488 


38 


2-0391649 


2-1047652 


2-1754113 


2-2516741 


2-3342152 


2-4238044 


39 


20402197 


2-1058998 


2-1766346 


2-2529964 


2-3?56482 


2-4253622 


40 


2-0412757 


2-1070359 


2-1778595 


2-2543204 


2-3370833 


2-4269222 


41 


20423330 


2-1081733 


2-1790859 


2 2556461 


2-3385203 


2-4284844 


19 
18 
17 
16 
15 


42 


20433916 


2-1093121 


21803139 


2-2569736 


2-3399593 


2-4300489 


43 


2-0444515 


2-1104523 


2-1815435 


2-2583029 


2-3414002 


2-4316155 


44 


20455126 


2-1115940 


2-1827746 


2-2596339 


2-3428432 


2-4331844 


45 


20465750 


2-1127371 


2-1840074 


2-2609667 


2-3442881 


2-4347555 


46 


2-0476386 


2-1138815 


2-1852417 


2-2623012 


2-3457349 


2-4363289 


14 
13 
12 
11 
10 


47 


2-0487036 


21150274 


2-1864775 


2-2636376 


2-3471838 


2-4379045 


48 


20497698 


2-1161748 


2-1877150 


2-2649756 


2-3486347 


2-4394823 


49 


20508373 


21173235 


2-1889541 


2-2663155 


2-3500875 


2-4410624 


50 


2-05190G1 


2-118*737 


2-1901947 


2-2676571 


2-3515424 


2-4426448 


51 


2-0529762 


2-1196253 


21914370 


2-2690005 


2-3529992 


2-4442294 


9 
8 
7 
6 
5 


52 


20540476 


2-1207783 


2-1926808 


2-2703457 


2-3544581 


2-4458163 


53 


2-0551203 


21219328 


2-1939262 


2-2716927 


2-3559189 


2-4474054 


54 
65 


20561942 


2-1230887 


2-1951733 


2-2730415 


2-3573818 


2-4489968 


20572695 


2-1242460 


2-1964219 


22743921 


2-3588467 


2-4505905 


56 


20583460 


2-1254048 


2-1976721 


2-2757445 


2-3603136 


2-4521865 


4 
3 
3 

1 



57 


20594239 


2-1265651 


21989240 


2-2770987 


2-3617826 


2-4537848 


58 


2-0G05031 


21277267 


2-2001775 


2-2784546 


2-363-2535 


2-4553853 


59 


20615836 


2-1288899 


2-2014326 


2-2798124 


2-3647-265 


2-4569882 


CO 


2-06-2665S 


2-1300545 


2-2026893 


2-2311720 


2^66^:016 


2-4585933 


/ 


29' 


28'* 


27' 


26» 


26'' 


24* 








Cosecants. 


r 











SECANTS AMTl 


roRP/v 


V KTJ^. 




4^.^ 


, 






Secants. 








66'* 


67° 


68° 


69° 


70' 


71° 


/ 




2-45859'5S 


2-5593047 


2-6694672 


2-7904281 


2-9928044 
2-9-2^1431 


2-0715035 


60 




2'4C02008 


2-5610599 


2 6713906 


2-7925444 


30741507 


59 




2 4618106 


2-5628176 


2-6733171 


2-7946641 


2-923-1M8 


3-0767525 


58 




2-4534227 


2-5645781 


2-6752465 


2-7967873 


2'930832G 


3-0793590 


57 




2-4C00371 


2-5663412 


2-6771790 


2-7989140 


2-9331833 


3-08iy702 


60 




2-4CGG538 


2-5681069 


2-6791145 


2-8010441 


2-9355380 


3-0845b60 


55 




2-4fi82729 


2-5698752 


2-6810530 


2-8031777 


2-9378968 


3-0872066 


51 




2'4(J9S913 


2-5716462 


2-6829945 


2-8053148 


2-9402597 


3-0898319 


53 




2-4715181 


2-5734199 


2-6849391 


2-8074554. 


2-9126265 


3-0924620 


52 




2-4731442 


2-5751963 


2-6868867 


2-8095995 


2-9449975 


3-095 ir67 


51 




2-4747726 


2-5769753 


2-6888374 


2-8117471 


2-9473725 


30977363 


50 




2-4764034 


2-5787570 


2-6907912 


2-8138982 


2-9497516 


3-1003805 


49 




2-4780366 


2-5805114 


2-6927480 


2-8160529 


2-9521348 


3-1030296 


48 




2-4796721 


2-5823284 


2-6947079 


2-8182111 


2-9545221 


3-1056835 


47 




2-4813100 


2-5841182 


2-6966709 


2-8203729 


2-9569135 


3-10d342-2 


46 




2-4829503 


2-5859107 


2-6986370 


2-8225382 


2 9593090 


3-1110057 


45 




2 1845929 


2-5877058 


2-7006061 


2-8247071 


2-9617087 


3-1136740 


44 




2 4862380 


2-5895037 


2-7025784 


2-8268796 


2-9611125 


31163472 


43 




2-4878854 


2-5913043 


2-7045538 


2-8290556 


2-9665-205 


3-1190252 


42 




2-4895352 


2-5931077 


2-7065323 


2-831235S 


2-9fi89327 


3-1217081 


41 




2-4911874 


2-5949137 


2-7085139 


2-8334185 


2^9713490 


3-1243959 


*0 




2-4928421 


2-5967225 


2-7104987 


2-8356054 


2-9737695 


3-1270886 


39 




2*494499 f 


2-5985341 


2-7124866 


2-8377958 


2-9761942 


3 1297862 


38 




2-4961586 


2-6003484 


2-7144777 


2-8399899 


2 9786231 


3-1321887 


37 




2-4978204 


2-6021654 


2-7164719 


2-8421877 


2-9810563 


3-1351962 


36 


25 


2-4994848 


2-6039852 


2-7184693 


2-8443891 


2-9834936 


3-1379086 


35 


26 


2-5011515 


2-C058078 


2-7204698 


2-8465941 


2-9859352 


3-1406259 


34 


27 


2-5028207 


2-6076332 


2-7224735 


2-84880-28 


2-98838U 


3-1433483 


33 


28 


2-5044923 


2-6094613 


2-7244S04 


2-8510152 


2-9908312 


3-1460756 


32 


29 


2-5061663 


2-6112922 


2-7261905 


2-8532312 


2-9932856 


3-1486079 


31 


30 


2-a078428 


2-6131259 


2-7285038 


2-8554510 


2-9957443 


3-1515453 


30 


31 


2-5095218 


2-61496-24 


2-7305203 


2-8576744 


2-9982073 


3-1542877 


29 


32 


2-5112032 


2-6168018 


2-7325400 


2-8599015 


3-0006746 


3-1570351 


28 


83 


2-5128871 


2-6186439 


2-7345630 


2-8621324 


3-0031462 


3-1597876 


27 


Si 


2-6145735 


2-6204888 


2-736o8y2 


2-8643670 


3-0056221 


3-1625452 


26 


35 


2-5162624 


2-6223366 


2-7386186 


2-8666053 


3-0081024 


3-1653078 


25 


36 


2-5179537 


2-6241872 


2-7406512 


2-8688474 


30105870 


3-1680756 


24 


37 


2-5196475 


2-6260406 


2-7426871 


2-8710932 


3-0130760 


3-1708484 


23 


33 
39 
10 


2-5213438 


2-6278969 


2-7447-263 


2-8733428 


3-0155694 


3-1736-264 


22 


2-523042G 


2-6297560 


2-7467687 


2-8755961 


3-0180672 


3-1764095L' 


21 


2-6247440 


2-S316180 


2-7488144 


2-8776532 


3 0205693 


3-1791978 


20 


41 
42 


2-52G4478 


2-6334828 


2-7508634 


2-8801142 


3-0230759 


3-1819913 


19 


2-5281541 


2-6353506 


2-7529157 


2-8ii23789 


3-0255868 


3-1847899 


18 


43 


2-5298630 


2-6372211 


2-7549712 


2-8846474 


3-C -281023 


3-1875937 


17 


44 


2-5315744 


2-6390946 


2-7570301 


2-8S69198 


3-0306221 


319040-28 


16 


45 


25332883 


2-6409710 


2-7590923 


2-8891960 


30331464 


3-1932170 


15 


46 


2-5350048 


2-6428502 


2-7611578 


2-8914760 


3-0356752 


3-1960365 


14 


47 


2-5367238 


2-6447323 


2-7632267 


2-8937598 


3-038-2084 


3-ly8b613 


13 


48 


2-5384453 


2-6466174 


2-7652988 


2-8960475 


30407462 


3-2016913 


12 


49 


2-5401694 


2-6485054 


2-7673744 


2-8983391 


3-0432884 


3-2045266 


11 


50 


2-5418961 


2-6503962 


2-7694532 


2-9006346 


3-0458352 


3-2073673 


10 


51 


2-5436253 


2-6522901 


2-7715355 


2-9029339 


3-0483864 


3-2102132 


9 


52 


2-5453571 


2-6541868 


2-7736211 


2-9052372 


3-0509423 


3-2130644 


8 


53 


2-5470915 


2-6560865 


2-7757100 


2-9075443 


30535026 


3-2159210 


7 


54 


2-5488284 


2-6579891 


2-7778024 


2-9098553 


3-0560675 


3-2187830 


6 


55 


2-5505680 


2-6598947 


2-7798982 


2-9121703 


30586370 


3-2216503 


5 


56 


2-5523101 


2-6618033 


2-781.9973 


2-9144892 


30612111 


3-2245230 


4 


57 
58 


2-5540548 


2-6637148 


2-7840999 


2-9168121 


3-0(.37898 


3-2274011 


3 


2-5558022 


2-6656292 


2-7862059 


2-9191389 


306G3731 


3-2302i46 


S 


59 
60 


2-5575521 


2-6675167 


2-7883153 


2-92H697 


3 0i)b9610 


3-2331736 


1 


2-5593047 


2-6694672 


2-7904281 


2-9238044 


3 0715535 


3-2360680 





/ 


i ??° 


22- 


21° 


20° 


ir 


18' 


/ 






Cosecants. 







484 




SECAiTTS Altt) OOSEuAiTTg. 






9 






Secants. 








IT 


73^ 


w 


75** 


76* 


77* 





3-2360680 


3-4203036 


3-6279553 


3-8637033 


4-1335655 


44454115 


60 


1 


3-2389()78 


3-4 -235611 


3-6316395 


3-86790-25 


4-13S3939 


4-4510198 


59 


2 


3-2418732 


3-426S-251 


3-63535 J 6 


3-8721112 


4-143-2339 


4-45664-28 


58 


3 


3-2447840 


3-430095S 


3-6390315 


3-8763293 


4-1480856 


4-4622803 


57 


4 


3-2477003 


3-4333727 


3-6427392 


3-8805570 


4-15--'9491- 


4-46793-24 


56 


5 


3-2506222 


3-4366563 


3-6464548 


3-8847943 


4-1578243 


4-4735993 


55 


6 


3-2535496 


3-4399465 


3-6501783 


3-8890411 


4-16271U 


4-4792810 


54 


7 


3-2564825 


3-443-2433 


3-6539097 


3-8932976 


4-1676102 


4-4819775 


53 


8 


3-25942U 


3-4465467 


3-6576491 


3-8975637 


4'17-25210 


4-4906889 


52 


9 


3 2623652 


3-44985(i8 


3-6613964 


3-9018395 


4-1774438 


44964152 


51 


10 


3-2653119 


3-4531735 


3-6651513 


3-9061250 


4-1823785 


4-5021565 


50 


11 


3-2682703 


3-4564969 


3-6689151 


3-9104203 


4-1873252 


4-50791-29 


49 


12 


3-271-2311 


3-4598-269 


3-67-26865 


3-9147-254 


4-192'2840 


4-5136814 


48 


13 


3-2741977 


3-4631G37 


3-6764660 


3-9190403 


4-197-2549 


4-5194711 


47 


14 


3-2771700 


3-4665073 


3-6802536 


3-9233651 


4-20-22380 


4-5252730 


46 


15 


3-2801479 


3-4698576 


3.-6840493 


3-9276997 


4-2072333 


4-5310903 


45 


16 


3-2831316 


3-4732146 


3-6878532 


3-9320443 


4-2122408 


4-5369229 


44 


17 


3-2861209 


3-4765785 


3-6916652 


3-9363988 


4-2172606 


4-54-27709 


43 


18 


3-2891160 


3-4799492 


3-6954854 


3-9407633 


4-2J*2928 


4-5486344 


42 


19 


3-2921168 


3-4833267 


3-6993139 


3-9451379 


4-227i^73 


4-5545134* 


41 


20 


3-2951234 


3-4867110 


3-7031506 


3-9495224 


4-2323943 


4-5604080 


40 


21 


3-2981357 


3-4901023 


3-7069955 


3-9539171 


4-2374637 


4-5fJ63183 


39 


22 


3-3011539 


3-4935004 


3-7108489 


3-9583219 


4-2425457 


4-57-22444 


38 


23 


3-3041778 


3-4969055 


3-7147105 


3-96-27369 


4-2476402 


45781862 


37 


24 


3-307-2076 


3-5003175 


3-7185805 


3-9671621 


4-2527474 


4-584l4?9 


36 


25 


3-3102432 


3-5037365 


3-7224589 


3-9715975 


4-2578671 


4-590' r< 4 


35 


26 


3-3132347 


3-5071625 


3-7263457 


3-9760431 


4-2629996 


4-5961070 


34 


27 


3-31633-20 


3-5105954 


3-7302409 


3-9804991 


4-2681449 


4-6021126 


33 


28 


3-3193853 


3-5140354 


3-7341446 


3-9849654 


4-2733029 


4-6081343 


32 


29 


3-3224444 


3-51748-24 


3-738056S 


3-9894^21 


4-2784733 


4-61417-22 


31 


30 


3-3255095 


3-5209365 


3-7419775 


3-9939292 


4-2836576 


4-6202263 


30 


31 


3-3285805 


3-5243977 


3-7459063 


3-9984267 


4-2888543 


4-626296? 


29 


32 


3-3316575 


3-5278660 


3-7498447 


4-00-29347 


4-2940640 


4-6323835 


28 


33 


3-3347405 


3-5313414 


3-7537911 


4-0074532 


4-2992867 


4-6384867 


27 


34 


3-3378294 


3-5348240 


3-7577462 


4-01198-23 


4-30452-25 


4-6446064 


26 


85 


3-3409214 


3-5383138 


3-7617100 


4-0165219 


4-3097715 


4-6507427 


25 


36 


3-3440254 


3-5418107 


3-7656821 


4-02107-22 


4-3150336 


4-6568956 


24 


37 


3-34713-24 


3-5453149 


3-7696636 


4-0256332 


4-3203090 


4-6630652 


23 


6% 


3-3502455 


3-54882<« 


3-7736535 


4-0302048 


4-3-255977 


4-6692516 


22 


39 


3-3533647 


3-5523450 


3-7776522 


4-0347872 


4-3308996 


4-6754548 


21 


40 


3-3564900 


3-5558710 


3-7816596 


4-0393804 


4-3362150 


4-6816748 


20 


41 


3-3596214 


3-5594042 


3-7856760 


4-0439844 


4-3415438 


4-6879119 


19 


42 


3-3627589 


3-5629448 


3-7897011 


4-0485992 


4-3468861 


4-6941660 


18 


43 


3-36590-26 


3-56619-28 


3-7937352 


4-0532-249 


4-3522419 


4-7004372 


17 


44 


3-3690524 


3-5700481 


3-7977782 


4-0578615 


4-3576113 


4-7067256 


16 


45 


3-372-2084 


3-5736108 


3-8018301 


4-06-25091 


4-36-29943 


4-7130313 


15 


46 


3-3753707 


3-5771810 


3-8058911 


40671677 


4-3683910 


4-7193542 


14 


47 


3-3785391 


3-5807586 


3-8099610 


4-0718374 


4-3738015 


4-7256945 


13 


48 


3-3817138 


3-5843437 


3-8140399 


4-0765181 


4-3792257 


4-73205-24 


12 


49 


3-3848948 


3-5879362 


3-8181280 


4-0812100 


4-3846638 


4-7384277 


11 


50 


3-38808-20 


3-5915363 


3-822-2251 


4 -0859 MO 


4-3901158 


4-7448206 


10 


51 


3-3912755 


3-5951439 


3-8263313 


4-0900272 


4-3955817 


4-7512312 


9 


52 


3-3944754 


3-5987590 


3-8304467 


4 0953526 


4-4010616 


4-7576596 


8 


53 


3-3976816 


3-6023818 


3-8345713 


4- 1000893 


4-4065556 


4-7641058 


7 


54 


3-4008941 


3-6060121 


3-8387052 


4 1048374 


4-4120637 


4-7705699 


6 


55 


3-4041130 


3-6096501 


3-8428482 


4-1095967 


4-4175859 


4-7770519 


5 


56 


3-4073382 


3-613-2957 


3-8470006 


41143(;75 


4-4231224 


4-7835520 


4 


' 57 


3-41056'J9 


3-6169490 


3-8511622 


41191498 


4-4286731 


4-7900702 


3 


58 


3-4138080 


3-6-206101 


3 85M332 


4-1-239435 


4-4342382 


4-7966066 


S 


69 


3-4170526 


3-624-27a8 


3-8595135 


4-1-287487 


4-4398176 


48031613 


1 


60 


3-4203036 


3-6279553 


3-8637033 


4-1335655 


4-4454115 


4-8097343 





"1 


17' 


16' 


16' 


14" 


13' 


12' 


/ 






Cosecants. 











SKCAKTS Aisrt) 


COSEOAKTS. 




485 


/ 






Secants. 








78* 


79' 


80** 


8r 


82' 


BT 


' 





4-80973^3 


5-2408431 


5-7587705 


6-3924532 


7-1852965 


8-205505>0 


60 


1 


4-8163258 


5-2486979 


5-768-2867 


6-4042154 


7-2001996 


8-2249962 


50 


2 


4-8229357 


5-2565768 


5-7778330 


6-4160216 


7ia61663 


8-2446748 


68 


3 


4-8295643 


6-2644798 


6-7874153 


6-4278719 


7-2301940 


8-2642483 


57 


4 


4-8362114 


6-2724070 


5-7970280 


6-4397666 


7-2462859 


8-2840171 


50 


5 


4-8428774 


5-2803587 . 


5-8066732 


6-4517059 


7-2604417 


8-3038812 


55 


6 


4-8495621 


6-2883347 


6-8163510 


6-4636901 


7-2756616 


8-3238415 


54 


7 


4-8562657 


5-2963354 


5-8260617 


6-4757195 


7-2909460 


8-3438986 


63 


8 


. 4-6629883 


5-3043608 


5-8358053 


6-4877944 


7-3062964 


8-3640534 


52 


9 


4-8697299 


6-3121109 


5-8465820 


6-4999148 


7-3217102 


8-3843065 


51 


10 


4-8764907 


6-3:i04860 


5-8553921 


6-5120812 


7-3371909 . 


8-4046586 


50 


11 


4-8832707 


6-3285861 


5-8652356 


6-5242938 


7-3527377 


8-4251105 


49 


12 


4-8900700 


6-3367114 


5-8751128 


6-5365528 


7-3683512 


8-4466629 


48 


13 


4-8968886 


6-3448620 


5-8850238 


6-5488686 


7-3840318 


8-4663165 


47 


14 


4-9037267 


6-3530379 


5-8949688 


6-5612113 


7-3997798 


8-4870721 


46 


15 


" 4-9105844 


6-3612393 


6-9049479 


6-5736112 


7-4155969 


8-5079304 


45 


16 


4-9174616 


6-3694664 


5-9149614 


6-5860587 


7-4314803 


8-5288923 


44 


17 


4-9243686 


6-3777192 


6-9250095, 


6-5985540 


7-4474335 


8-5499584 


43 


18 


4-9312754 


6-3859979 


5-9350922 


6-6lU>973 


7-4G31660 


8-5711295 


42 


19 


4-9382120 


6-3943026 


6-9452098 


6-6236S90 


7-4796482 


8-5924065 


41 


20 


4-9451687 


6-4026333 


6-9553625 


6-6363-293 


7-4957106 


8-6137901 


40 


21 


4-9521453 


6-4109903 


5-9655504 


6-6490184 


7-5119437 


8-6352812 


39 


22 


4-9591421 


5-4193737 


6-9757737 


6-6617568 


7-5282478 


8-6568805 


38 


23 


4-9661591 


6-4277835 


6-9860326 


6-6746446 


7-5446236 


8-6785889 


37 


24 


4-9731964 


6-4362199 


5-9963274 


6-6873822 


7-5610713 


8-7004071 


36 


25 


4-9d02541 


6-4446831 


6-0066581 


6-7002699 


7-5775916 


8-7223361 


35 


26 


4-9873323 


5-4531731 


6-0170250 


6-7132079 


7-5941849 


8-7443766 


34 


27 


4-9944311 


6-4616901 


6-0274282 


6-7261965 
6-7392360 


7-6108516 


8-7665295 


33 


28 


6-0015505 


6-4702342 


6-0378680 


7-6275923 


8-7887957 


32 


29 


5-0086907 


6-4788056 


6-0483445 


0-7323268 


7-6444075 


8-8111761 


31 


30 


6-0158517 


6-4874043 


6-0588580 


6*7854691 


7-6612976 


8-8336715 


30 


31 


6-0230337 


6-4960305 


6-0694085 


0^786632 


7-678-2631 


8-8562828 


29 


32 


6-0302367 


6-5046843 


6-0799964 


6'7919095 


7-6953047 


8-8790109 


28 


33 


6-0374607 


6-5133659 


6-0906219 


6-8052082 


7-71242-27 


8-8018567 


27 


34 


6-0447060 


6-5220754 


6-1012850 


6-8185697 


7-7296176 


8-9248211 


26 


35 


6-0519726 


6-5308129 


6-1119861 


6-8319642 


7-7468901 


8-9479051 


25 


36 


5-0592606 


6-5395786 


6-1227253 


6-8454222 


7-7642406 


8-9711095 


24 


37 


5-0665701 


6-5483726 


6-1335028 


6-8589338 


7-7816697 


8-9944354 


23 


38 


6-0739012 


6-5571951 


6-1443189 


6-8724995 


7-7991778 


9-0178837 


22 


39 


5-0812539 


•5-5660460 


6-1551736 


6-8861195 


7-8167656 


90414663 


21 


40 


6-0886284 


6-5749258 


6-1660674 


6-8997942 


7-8344335 


fi-0651512 


20 


41 


6-0960248 


6-5838343 


6-1770003 


6-9135239 


7-8521821 


9-0889725 


19 


42 


61034431 


5-5927719 


6-1879725 


6-9273089 


7-8700120 


9-1129200 


18 


43 


6-1108835 


6-6017386 


6-1989843 


6-9411496 


7-8879238 


9-1369949 


17 


44 


6-1183461 


6-6107345 


6-2100359 


6-9550464 


7-9059179 


9-1611980 


16 


45 


6-1258309 


8-6197599 


6-2211275 


6-9689994 


7-9239950 


9-1855305 


15 


46 


6-1333381 


6-6288148 


6-2322594 


6-9830092 


7-9421556 


9-2699934 


14 


47 


6-1408677 


6-6378995 


6-2434316 


6-9970760 


7-9604003 


9-2345877 


13 


48 


6-1484199 


6-6470140 


6-2546446 


7-0112001 


7-9787298 


9-2593145 


12 


49 


6-1559948 


6-6561584 


6-2668984 


7-0253820 


7-9971445 


9-2841749 


11 


50 


61635924 


6-6653331 


6-2771933 


7-0396220 


8-0166450 


9-3091699 


10 


51 
62 
53 
54 


6-1712128 


6-6745380 


6-2885295 


7-0539205 


80342321 


9-3343006 


9 


6-1788563 


6-6837734 


6-2999073 


7-0682777 


8-0529062 


9-35950-82 


8 


6-1865228 


6-6930393 


6-3113269 


7-0826941 


8-0716681 


9-3849738 


7 


6-19J2125 


5-7023360 


6-3227884 


7-0971700 


8-0905182 


9-4106184 


6 


55 


6-2019251 , 


^•7116636 


6-3342923 


7-1117059 


8-1094573 


9-4362033 


6 


56 
67 
68 
69 
60 


6-20966^8 


5-7210223 


6-3458386 


7-1263019 


8-1284860 


9-4620296 


4 


6-2174216 


6-7304121 


6-3674276 


7-1409687 


8-1476048 


9-4879984 


3 


6-2252050 


6-7398333 


6-3690695 


7-1536764 


8-1668145 


9-6141110 


2 


6-2330121 


6-7492861 


6-3807347 


7-1704666 


8-1861167 


9-5403686 


1 


6-2408431 


6-7687705 


6-3024532 


7-1862965 


8-20560yO 


9 -56677^2 







11* 


10' 


r 


8» 


r 


6" 


/ 






Cosecants. 







486 



SECANTS AND COSECANTS. 



/ 






Secants. 








84' 


85' 


86- 


8r 


88- 


89' 


1 




9-5667722 


11-473713 


14-335587 


19-107323 


28-653708 


57-298688 


CO 




9-5933233 


11-511990 


14-395471 


19-213970 


28-894398 


58-269755 


89 




9-6200229 


11-550523 


14-455859 


19-321816 


29-139169 


59-274308 


80 




9-646872i 


11-589316 


14-516757 


19-430882 


29-388124 


60-314110 


67 i, 




9-6738730 


11-628372 


14-578172 


19-541187 


29-641373 


61-391050 


86 




9-7010260 


11-667693 


14-640109 


19-652754 


29-899026 


62-507153 


65 




9-7283327 


11-707282 


14-702576 


19-765604 


30161201 


63-664595 


54 




9-7557944 


11-747141 


14-765580 


19-879758 


30-428017 


64-865716 


83 




9-7834124 


11-787274 


14-8-29128 


19-995241 


30-699598 


66113036 


52 




9-8111880 


11-827683 


14-893226 


20-112075 


30-976074 


67-409272 


51 




9-8391227 


11-868370 


14-957882 


20-230284 


31-257577 


68-757360 


60 




9-8672176 


11-909340 


15-023103 


20-349893 


31-544246 


70-160474 


49 




9-8954744 


11-950595 


15-088896 


20-470925 


31-836225 


71-622052 


43 




9-9238943 


11-992137 


15-155270 


20-593409 


32133663 


73-145827 


47 




9-9524787* 


12-033970 


15-222231 


20-717368 


32-436713 


74-735856 


4S 




9-9812291 


12-076098 


15-289788 


20-842830 


32-745537 


76-396554 


45 




10010147 


12118522 


15-357949 


20-969824 


33-060300 


78-132742 


44 




10039234 


12-161245 


15-4267-21 


21-098376 


33-381175 


79-949684 


43 




10-068491 


12-204274 


15-496114 


21 •2-28515 


33-708345 


81-853150 


42 




10-097920 


12-247608 


15-566135 


21-360272 


34 041994 


fe3-849470 


41 


80 


10-127522 


12-291252 


15-636793 


21-493676 


34-382316 


85-945609 


40 


21 


10-157300 


12-335210 


15-708096 


21-628759 


34-729515 


88-149244 


39 


22 


10-187254 


12-37J484 


15-780054 


21-765553 


35-083800 


90-468863 


38 


23 


10-217386 


12-424078 


15-852676 


21-904090 


35-445391 


92-913869 


37 


24 


10-247697 


12-468995 


15-925971 


22044403 


35-814517 


95-494711 


35 


25 


10-278190 


12-514240 


15-999948 


22-186528 


36-191414 


98-2-23033 


35 


26 


10-308866 


12-559815 


16-074017 


22-330499 


36-576332 


101-11185 


34 


27 


10-33972G 


12-6057-24 


16-149987 


22-476353 


36-969528 


104-17574 


33 


28 


10-370772 


12-651971 


16-226069 


22-624126 


37-371273 


107-43114 


32 


29 


10-402007 


12-698560 


16-302873 


22-773857 


37-781849 


110-89656 


31 


30 


10-433431 


12-745495 


16-380408 


22-925586 


38-201550 


114-59301 


30 


81 


10-465046 


12-792779 


16-458686 


23-079351 


38-630683 


118-54440 


29 


32 


10-496854 


12-840416 


16-537717 


23-235196 


39-069571 


122-77803 


28 


33 


10-5-J8857 


12-888410 


16-617512 


23-393161 


39-518549 


127-32526 


27 


34 


10-561057 


12-936765 


16-698082 


23-553291 


39-977969 


132-22229 


26 


35 


10-593455 


12-985486 


16-779439 


23-715630 


40-448201 


137-51108 


25 


36 


10-626054 


13-034576 


16-861594 


23-8802-24 


40-929630 


143-24061 


24 


37 


10-658854 


13-084040 


16-944559 


24-047121 


41-422660 


149-46837 


23 


38 


10-691859 


13-133882 


17-028346 


24-216370 


41-927717 


156-262-28 


22 


39 


10-725070 


13-184106 


17-112966 


24-388020 


42 445245 


163-70325 


21 


40 


10-758488 


13-234717 


17-198434 


24-562123 


42-975713 


171-88831 


20 


41 


10-792117 


13-285719 


17-284761 


24-738731 


43-519612 


180-93496 


19 


42 


10-825957 


13-337116 


17-371960 


24-917900 


44-0774^8 


190-98680 


18 


43 


10-860011 


13-388914 


17-460046 


25-099685 


44-64979i> 


202-22122 


17 


44 


10-894281 


13-441118 


17-549030 


25-284144 


45-237195 


214-85995 


16 


45 


10-928768 


13-493731 


17-638928 


25-471337 


45-840260 


229-18385 


15 


46 


10-963475 


13-546758 


17-729753 


25-661324 


46-459625 


245-55402 


14 


47 


10-998406 


13-600205 


17-821520 


25-854169 


47-095961 


264-44269 


13 


48 


11-033560 


13-654077 


17-914243 


26-049937 


47-749974 


286-47948 


12 


49 


11-068940 


13-708379 


18-007937 


26-248694 


48422411 


312-52297 


11 


SO 


11-104549 


13-763115 


18-102619 


26-450510 


49-114062 


343-77516 


10 


61 


11-140389 


13-818291 


18-198303 


26-655455 


49-825762 


381-97230 





82 


11 176462 


13-873913 


18-295005 


26-863603 


80-558396 


429-71873 


8 


63 


11-212770 


13-929985 


18-392742 


27075030 


51-312902 


491 10702 


7 


54 


11-249316 


13-986514 


18-491530 


27-289814 


82-090272 


572-95809 


6 


55 


11-286101 


14-043504 


18-591387 


27-508035 


82-891564 


087-54960 


5 


M 


11-323129 


14-100963 


18-692330 


27-729777 


53-717896 


859-43689 


4 


! 57 


11-360402 


14-158894 


18-794377 


27-955125 


84-570464 


1145-9157 


3 


I 88 


11-397922 


14-217304 


18-897545 


28-184168 


85-450534 


1718-8735 


S 


89 


ll-43569i 


14-276-200 


19-001854 


28-410997 


86-359462 


3437-7468 


1 


' 60 


11-473711 


14-335587 


19-107323 


28-653708 


87-298683 


Infinite. 





/ 


6* 


4- 


3- 


2" 


V 


0* 


i 








Cosecants. 






t— 

















Table 85 —NATURAL tancients and cotakgents. 



0^ 


1° ! 


Tang 

.00000 


Cotang 


Tang 
.01746 


Cotang 

57.2900 


Infinite. 


.00029 


3437.75 


.01775 


56.3506 


.00058 


1718.87 


.01804 


55.4415 


.00087 


1145.92 


.01833 


54.5613 


.00116 


859.436 


.01862 


53.7086 


.00145 


687.549 


.01891 


52.8821 


.00175 


572.957 


.01920 


52.0807 


.00204 


491.106 


.01949 


51.3032 


.00233 


429.718 


.01978 


50.5485 


.00262 


381.971 


.02007 


49.8157 


.00291 


343.774 


.02036 


49.1039 


.00320 ' 


312.521 


.02066 


48.4121 


.00349 


286.478 


.02095 


47.7395 


.00378 


264.441 


.02124 


47.0853 


.00407 


245.552 


.02153 


46.4489 


.00436 


229.182 


.02182 


45.8294 


.00465 


214.858 


.02211 


45.2261 


.00495 


202.219 


.02240 


44.6386 


.00524 


190.984 


.02269 


44.0661 


.00553 


180.932 


.02298 


43.5081 


.00582 


171.885 


.02328 


42.9641 


.00611 


163.700 


.02357 


42.4335 


.00640 


156.259 


.02386 


41.9158 


.00669 


149.465 


.02415 


41.4106 


.00698 


143.237 


.02444 


40.9174 


.00727 


137.507 


.02473 


40.4358 


.00756 


132.219 


,02502 


39.9055 


.00785 


127.321 


.02531 


39.5059 


.00815 


122.774 


.02560 


39.0568 


.00844 


118.540 


.02589 


38.0177 


.00873 


114.589 


.02619 


38.1885 


.00902 


110.892 


.02648 


37.7686 


.00931 


107.426 


.02677 


37.3579 


.00960 


104.171 


.02706 


36.9560 


.00989 


101.107 


.02735 


36.5627 


.01018 


98.2179 


.02764 


36.1776 


.01047 


95.4895 


.02793 


35.8006 


.01076 


92.9085 


.02822 


35.4313 


.01105 


90.4633 


.02851 


35.0695 


.01135 


88.1436 


.02881 


34.7151 


.01164 


85.9398 


.02910 


34.3678 


.01193 


83.8435 


.02939 


34.0273 


.01222 


81.8470 


.02968 


33.6935 


.01251 


79.9434 


.02997 


33.3662 


.01280 


78.1263 


.03026 


33.0452 


.01309 


76.3900 


.03055 


32.7303 


.01338 


74.7292 


.03084 


32.4213 


.01367 


73.1390 


.03114 


32.1181 


.01396 


71.6151 


.03143 


31.8205 


.01425 


70.1533 


.03172 


31.5284 


.01455 


68.7501 


.03201 


31.2416 


.01484 


67.4019 


.03230 


30.9599 


.01513 


66.1055 


.03259 


30.6833 


.01542 


64.8580 


.03288 


30.4116 


.01571 


03.6567 


.03317 


30.1446 


.01600 


62.4992 


.03346 


29.8823 


.01629 


61.3829 


.03376 


29.6245 


.01658 


60.3058 


.0:M05 


29.3711 


.01687 


59.2659 


.03434 


29.122G 


.01716 


58.2612 


.03463 


28.8771 


.01746 


57.2900 


.03492 
Cotang 


28.6363 
Tang 


Cotang 


Tang 


8 


9° 


8 


8° 



_Tang_ 
.03492 
.03521 
.03550 
.03579 
.03609 
.03638 
.03667 
.03696 
.03725 
.03754 
.03783 

.03812 
.03842 
.03871 
.03900 
.03929 
.03958 
.03987 
.04016 
.04046 
.04075 

.04104 
.04133 
.04162 
.04191 
.04220 
.04250 
.04279 
.04308 
.04337 
.04366 

.04395 
.04424 
.04454 
.04483 
.04512 
.04541 
.04570 
.04599 
.04628 
.04658 

.04687 
.04716 
.04745 
.04774 
.04803 
.04833 
.04862 
.04891 
.,04920 
.04949 

.04978 
.05:); 7 
.05037 
.05066 
.05095 
.05124 
.0515;^ 
.05182 
.05212 
.05241 
Cotang 



Cotang 



28.6363 
28.3994 
28.1004 
27.9372 
27.7117 
27.4899 
27.2715 
27.0566 
26.8450 
20.0C67 
26.4316 

26.2296 

26.0307 
25.8348 
25.6418 
25.4517 
25.2644 
25.0798 
24.8978 
24.7185 
24.5418 

24.3675 

24.1957 
24.0263 
23.8593 
23.6945 
23.5321 
23.3718 
23.2137 
23.0577 
22.9038 

22.7519 
22.6020 
22.4541 
22.3081 
22.1640 
22.0217 
21.8813 
21.7426 
21.6056 
21.4704 

21.3369 
21.2049 
21.0747 
20.9460 
20.8188 
20.6932 
20.5691 
20.4465 
20.3253 
20.2056 

20.0872 
19.9702 
19.8546 
19.7403 
19.6273 
19.5156 
19.4051 
19.2959 
19.1879 
19.0811 



Tang 



87'* 



Tang 



.05241 
.05270 
.05299 
.05328 
.05357 
.05387 
.05416 
.05445 
.05474 
.05503 
.05533 

.05562 
.05591 
.05620 
.05649 
.05678 
.05708 
.05737 
.05766 
.05795 
.05824 

.05854 
.05883 
.05912 
.05941 
.05970 
.05999 
.06029 
.06058 
.06087 
.06116 

.06145 
.06175 
.06204 
.06233 
.06262 
.06291 
.06321 
.06350 
.06379 
.06408 

.06437 

.06467 
.06496 
.06525 
.06554 
.06584 
.06613 
.06642 
.06671 
.06700 

.06730 
.06759 
.06788 
.06817 
.06847 
.06876 
.06905 
.06934 
.06963 
.06993 
Cotang I 



Cotang I 
19.0811 60 
18.9755 59 
18.8711 158 

18.7678 157 
18.6656 56 



18.5645 
18.4645 
18.3655 
18.2677 
18.1708 
18.0750 

17.9802 
17.8863 
17.7934 
17.7015 
17.6106 
17.5205 
17.4314 
17.3432 
17.2558 
17.1693 

17.0837 
16.9990 
16.9150 
16.8319 
16.7496 
16.6681 
16.5874 
16.5075 
16.4283 
16.3499 

16.2722 
16.1952 28 



16.1190 
16.0435 
15.9687 
15.8945 
15.8211 
15.7483 
15.6762 
15.6048 

15.5340 
15.4638 
15.3943 
15.3254 
15.2571 
15.1893 
15.1222 
15.0557 
14.9898 
14.9244 

14.8596 
14.7954 
14.7317 
14.6685 
14.6059 
14.5438 
14.4823 
14.4212 
14.3607 
14.3007 



Tanj^ 



86° 



487 



NATURAL TANGENTS AND COTANGENTS. 





40 




Tang 


Cotang 





.06993 


14.3007 


1 


.07022 


14.2411 


2 


.07051 


14.1821 


3 


.07080 


14.1235 


4 


.07110 


14.0655 


5 


.07139 


14.0079 


G 


.07168 


13.9507 




.07197 


13.8940 1 


8 


.07227 


13.8378 


9 


.07256 


13.7821 


10 


.07285 


13.7267 


11 


.07314 


13.6719 


12 


.07344 


13.6174 


13 


.07373 


13.5634 i 


14 


.07402 


13.5098 1 


15 


.07431 


13.4566 


10 


.07461 


13.4039 


17 


.07490 


13.3515 


18 


.07519 


13.2996 1 


19 


.07548 


13.2480 


20 


.07578 


13.1969 


21 


.07607 


13.1461 


22 


.07636 


13.0958 


%i 


.07665 


13.0458 


24 


.07695 


12.9962 


2.5 


.07724 


12.9469 


20 


.07753 


12.8981 


27 


.07782 


12.8496 


28 


.07812 


12.8014 


29 


.07841 


12.7536 


30 


.07870 


12.7062 


31 


.07899 


12.6591 


32 


.07929 


12.6124 


33 


.07958 


12.5060 


34 


.07987 


12.5199 


35 


.08017 


12.4742 


36 


.08046 


12.4288 


37 


.08075 


12.3838 


38 


.08104 


12.a390 


39 


.08134 


12.2946 


40 


.08163 


12.2505 


41 


.08192 


12.2067 


42 


.08221 


12.1632 1 


43 


.08251 


12.1201 1 


44 


.08280 


12.0772 


45 


.08309 


12.0346 1 


46 


.08339 


11.9923 1 


47 


.08368 


11.9504 1 


48. 


.08397 


11.9087 1 


49 


.08427 


11.8673 ! 


50 


.0iW56 


11.8262 


51 


.08485 


11.7853 


52 


.08514 


11.7448 


53 


.08.544 


11.7045 


54 


.0S573 


11.6^)45 


55 


.08602 


11.6248 


5() 


.08632 


11.5H.53 


57 


.08661 


11.5461 ' 


58 


.08690 


11 5072 


59 


.08720 


11.4('>H5 


CO 


.08749 


11.4301 1 


/ 


Cotang 


Tang 




8 


5° 1 



Tang 

.08749 
.08778 
.08807 
.08837 
.08866 
.08895 
.08925 
.08954 
.08983 
.09013 
.09042 

.09071 
.09101 
.09130 
.09159 
.09189 
.09218 
.09247 
.09277 



.09335 

.09365 
.09394 
.09423 
.09453 
.09482 
.09511 
.09541 
.09570 
.09600 
.09629 

.09658 
.09688 
.09717 
.09746 
.09776 
.09805 
.09834 
.09864 
.09893 
.09923 

.09952 
.09981 
.10011 
.10040 
.10069 
.10099 
.10128 
.10158 
!' .10187 
. 10216 

.10246 
.10275 
. 10305 
.10:^^4 
.103()3 
.10.S93 
. 10422 
. 10452 
. IO4.SI 
. 10510 
Cotang 



Cotang 
11.4:301 
11.3919 
11.3540 
11.3163 
11.2789 
11.2417 
11.2048 
11.1681 
11.1316 
11.0954 
11.0594 

11.0237 
10.9882 
10.9529 
10.9178 
10.8829 
10.8483 
10.8139 
10.7797 
10.7457 
10.7119 

10.6783 

10.6450 

10.6118 

10.5789 I 

10.5462 

10.5136 

10.4813 

10.4491 

10.4172 

10.3854 

10.3538 
10.3224 
10.2913 
10.2602 
10.2294 
10.1988 
10.1083 
10.1381 
10.1080 
10.0780 

10.0483 

10.0187 

9.98931 

9.96007 

9.93101 

9. -90211 

9.87338 

9.84482 

9.81641 I 

9.78817 

8.76009 
9.73217 
9.70441 
9.67680 
9.64935 
9.62205 
9.59490 
9.5()791 
9.54106 
9.51436 
Tang 



84° 



6° 


•J 


! 


Tang Cotang 
.10510 9.51436 


Tang 


Cotang 


.12278 


8.14435 


.10540 9.48781 


.12308 


8.12481 


.10509 


9.46141 


.12338 


8.10530 


.10599 


9.43515 


.12367 


8.08000 


.10628 


9.40904 


.12307 


8. 00074 


.10657 


9.38307 i 


.12426 


8.04756 


.10087 


9.35724 


.12456 


8.02848 


' .10716 


9.33155 


.12485 


8.00948 


.10746 


9.30599 


.12515 


7.99058 


.10775 


9.28058 


.12544 


7.97176 


i .10805 


9.25530 


.12574 


7.95302 


.10834 


9.23016 


.12603 


7.93438 


.10863 


9.20516 


.12033 


7.91582 


.10893 


9.18028 


.12062 


7.89734 


.10922 


9.15554 


.12692 


7.87895 


; .10952 


9.13093 


.12722 


7.86064 ' 


1 .10981 


9.10646 


.12751 


7.84242 


1 .11011 


9.08211 


.12781 


7.82428 


.11040 


9.05789 


.12810 


7.80622 


.11070 


9.03379 


.12^40 


7.78825 


.11099 


9.00983 


.12869 


7.77035 


.11128 


8.98598 


.12899 


7.75254 


.11158 


8.96227 


.12929 


7.73480 


.11187 


8.93867 


.12958 


7.71715 


.11217 


8.91520 


.12988 


7.69957 


.11246 


8.89185 


.13017 


7.68208 


.11276 


8.86862 


.13047 


7.66466 


.11305 


8.84551 


.13070 


7.64732 


.11335 


8.82252 


.13100 


7,63005 


i .11304 


8.79964 


.13130 


7.61287 


i .11394 


8.77689 


.13165 


7.59575 


.11423 


8.75425 


.13195 


7.57872 


.11452 


8.73172 


.13224 


7.56176 


; .11482 


8.70931 


.13254 


7.54487 


.11511 


8.68701 


.13284 


7.52806 


.11541 


8.66482 


.13313 


7.51132 


.11570 


8.64275 


.13343 


7.49465 


i .11600 


8.62078 


.1337-2 


7.47806 , 


' .11629 


8.59893 


.13402 


7.46154 


.IK • 


8.57718 


.13432 


7.44509 


.11688 


8.55555 


.13461 


7.42871 j 


: .11718 


{ 53402 


.13491 


7.41240 ! 


.11747 


8.51259 


.13521 


7.39616 ! 


.11777 


8.49128 


.ia550 


7.37999 : 


.11806 


8.47007 


.13580 


7.30389 1 


.11836 


8.44896 


.13609 


7.34786 


.11865 


8.42795 


.13639 


7.33190 


.11895 


8.40705 


.13669 


7.31600 I 


.11924 


8.38625 


.13698 


7.30018 : 


.11954 


8.36555 


.13728 


7.28442 


.11983 


8.34496 


.13758 


7.26873 


.12013 


8.32446 


.13787 


7.25310 


1 .12042 


8.30406 


.13817 


7.23754 


.12072 


8.28376 


.13846 


7.22204 


I .12101 


8.26355 


.13876 


7.20661 


i .12131 


8.24345 


.13906 


7.19125 


! .12160 


8.22344 


I .13935 


7.17594 


.12190 


8.20352 


i .13905 


7.16071 


.12219 


8.18370 


; .130r)5 


7.14553 


.12249 


8.16398 


! .14024 


7.13042 


j .12278 


8.14435 


.14054 
Cotang 


7.11537 


Cotang 


Tang 


Tang 


8 


3° 


8 


2° 



488 



NATURAL TANGENTS AND COTANGENTS. 







B° 




9° 


10° 


11° 






Tang 
.14054 


Cotang 


Tang 


Cotang 


Tang 
.17633 


Cotang 


Tang 1 Cotang 


60 





7.11537 


.15838 


6.31375 


5.67128 


.19438 


5.14455 


1 


.14084 


7.10038 


.15868 


6.30189 


.17663 


5.66165 


.19468 


5.13658 


59 


2 


.14113 


7.08.546 


.15898 


6.29007 


.17693 


5.65205 


.19498 


5.12862 


58 


3 


.14143 


7.07059 


.15928 


6.27829 


.17723 


5.64248 


.19529 


5.12069 


57 


4 


.14173 


7.05579 


.15958 


6.26655 


.17753 


5.63295 


.19559 


5.11279 


56 


5 


.14202 


7.04105 


.15988 


6.25486 


.17783 


5.62344 


.19589 


5.10490 


55 


6 


.14232 


7.02637 


.16017 


6.24321 


.17813 


5.61397 


.19619 


5.09704 


54 


7 


.14262 


7.01174 


.16047 


6.23160 


.17843 


5.60452 


.19649 


5.08921 


53 


8 


.14291 


6.99718 


.16077 


6.22003 


.17873 


5.59511 


.19680 


5.08139 


52 


9 


.14321 


6.98268 


.16107 


6.20851 


.17903 


5.58573 


.19710 


5.07360 


51 


10 


.14351 


6.96823 


.16137 


6.19703 


.17933 


5.57638 


.19740 


5.06584 


50 


11 


.14381 


6.95385 


.16167 


6.18559 


.17963 


5.56706 


.19770 


5.05809 


49 


12 


.14410 


6.93952 


.16196 


6.17419 


.17993 


5.5bVVV 


.19801 


5.05037 


48 


13 


.14440 


6.92525 


.16226 


6.16283 


.18023 


5.54851 


.19831 


5.042G7 


47 


14 


.14470 


6.91104 


.16256 


6.15151 


.18053 


5.53927 


.19861 


5.03499 


46 


15 


.14499 


6.89688 


.16286 


6.14023 


.18083 


5.53007 


.19891 


5.02734 


45 


16 


.14529 


6.88278 


.16316 


6.12899 


.18113 


5.52090 


.19921 


5.01971 


44 


17 


.14559 


6.86874 


.16346 


6.11779 


.18143 


5.51176 


.19952 


5.01210 


43 


18 


.14588 


6.85475 


.16376 


6.10664 


.18173 


5.50264 


.19982 


5.00451 


42 


19 


.14618 


6.84082 


.16405 


6.09552 


.18203 


5.49356 


.20012 


4.99695 


41 


20 


.14648 


6.82694 


.16435 


6.08444 


.18233 


5.48451 


.20042 


4.98940 


40 


21 


.14678 


6.81312 


.16465 


6.07340 


.18263 


5.47548 


.20073 


4.98188 


39 


22 


.14707 


6.79936 


.16495 


6.06240 


.18293 


5.46648 


.20103 


4.97438 


38 


23 


.14737 


6.78564 


.16525 


6.05143 


.18323 


5.45751 


.20133 


4.96690 


37 


24 


.14767 


6.77199 


.16555 


6.04051 


.18353 


5.44857 


.20164 


4.95945 


36 


25 


.14796 


6.75838 


.16585 


6.02962 


.18384 


5.43966 


.20194 


4.95201 


35 


26 


.14826 


6.74483 


.16615 


6.01878 


.18414 


5.43077 


.20224 


4.94460 


34 


27 


.14856 


6.73133 


.'16645 


6.00797 


.18444 


5.42192 


.20254 


4.93721 


33 


28 


.14886 


6.71789 


.16674 


5.99720 


.18474 


5.41309 


.20285 


4.02984 


32 


29 


.14915 


6.70450 


.16704 


5.98646 


.18504 


5.40429 


.20315 


4.92249 


31 


30 


.14945 


6.69116 


.16734 


5.97576 


.18534 


5.39552 


.20345 


4.91516 


30 


31 


.14975 


6.67787 


.16764 


5.96510 


.18564 


5.38677 


.20376 


4.90785 


29 


32 


.15005 


6.66463 


.16794 


5.95448 


.18594 


5.37805 


.20406 


4.90056 


28 


33 


.15034 


6.65144 


.16824 


5.94390 


.18624 


5.36936 


.20436 


4.89330 


27 


34 


.15064 


6.63831 


.16854 


5.93335 


.18654 


5.36070 


.20466 


4.88605 


26 


35 


.15094 


6.62523 


.16884 


5.92283 


.18684 


5.35206 


.20497 


4.87882 


25 


36 


.15124 


6.61219 


.16914 


5.91236 


.18714 


5.34345 


.20527 


4.87102 


24 


37 


.15153 


6.59921 


.16944 


5.90191 


.18745 


5.33487 


.20557 


4.86444 


23 


38 


.15183 


6.58627 


.16974 


5.89151 


.18775 


5.32631 


.20588 


4.85727 


22 


39 


.15213 


6.57339 


.17004 


5.88114 


.18805 


5.31778 


.20618 


4.85013 


21 


40 


.15243 


6.56055 


.17033 


5.87080 


.18835 


5.30928 


.20648 


4.84300 


20 


41 


.15272 


6.54777 


.17063 


5.86051 


.18865 


5.30080 


.20679 


4.83590 


19 


42 


.15302 


6.53503 


.17093 


5.85024 


.18895 


5.29235 


.20709 


4.82882 


18 


43 


.15332 


6.52234 


.17123 


5.84001 


.18925 


5.28393 


.20739 


4.82175 


17 


44 


.15362 


6.50970 


.17153 


5.82982 


.18955 


5.27553 


.20770 


4.81471 


16 


45 


.15391 


6.49710 


.17183 


5.81966 


.18986 


5.26715 


.20800 


4.80769 


15 


46 


.15421 


6.48456 


.17213 


5.80953 


.19016 


5.25880 


.20830 


4.80068 


14 


47 


.15451 


6.47206 


.17243 


5.79944 


.19046 


5.25048 


.20861 


4.79370 


13 


48 


.15481 


6.45961 


.17273 


5.78938 


.19076 


5.24218 


.20891 


4.78673 


12 


49 


.15511 


6.44720 


.17303 


5.77036 


.19106 


5.23391 


.20921 


4.77978 


11 


50 


.15540 


6.43484 


.17333 


5.76937 


.19136 


5.22566 


.20952 


4.77286 


10 


51 


.15570 


6.42253 


.17363 


5.75941 


.19166 


5.21744 


.20982 


4.76595 


9 


52 


.15600 


6.41026 


.17393 


5.74949 


.19197 


5.20925 


.21013 


4.75906 


8 


53 


.15630 


6.39804 


.17423 


5.73960 


.19227 


5.20107 


.21043 


4.75219 


7 


54 


.15660 


6.38587 


.17453 


5.72974 


.19257 


5.19293 


.21073 


4.74.534 


6 


55 


.15689 


6.37374 


.17483 


5.71992 


.19287 


5.18480 


.21104 


4.73851 


5 


56 


.15719 


6.36165 


.17513 


5.71013 


.19317 


5.17671 


.21134 


4.73170 


4 


57 


.15749 


6.34961 


.17543 


5.70037 


.19317 


5.16863 


.21164 


4.72490 


3 


58 


.1.5779 


6.33761 


.17573 


5.69064 


.1937'8 


5.16058 


.21195 


4.71813 


2 


59 


.1.5809 


6.32566 


.17603 


5.68094 


.19408 


5.15256 


.21225 


4.71187 


1 


60 


.15838 


6.31375 


.17633 


5.67128 


.19138 


5.14455 


.21256 


4.70463 


_0 

/ 




Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang Tang 




8P 1 


80° 1 


79° 1 


78° 



4b9 



NATURAL TANGENTS AND COTANGENTS. 



/ 

1) 


12° 


i 13° 


i 14° 1 


15° 




Tang 

.21250 


Cotang 


Tang 

.23087" 


Cotang 
4.33148 


Tang 


Cotang 1 


Tang 1 Cotang 


/ 


4.70403 


.24933 


4.01078 1 


.26795 


3.73205 


60 


1 


.21286 


4.09791 


.23117 


4.32573 


.24904 


4.00582 1 


.26826 


3.72771 


59 


2 


.21316 


4.09121 


.23148 


4.32001 


.24995 


4.00080 


.26857 


3.72338 


58 


3 


.21347 


4.08452 


.23179 


4.31430 


.25020 


3.99592 


.26888 


3.71907 


57 


4 


.21377 


4.07786 


.23209 


4.30860 


.25050 


3.99099 


.26920 


3.71476 


56 


5 


.21408 


4.67121 


.23240 


4.30291 


.25087 


3.98007 


.26951 


3.71046 


55 


6 


.21438 


4.06458 


.23271 


4.29724 


.25118 


3.98117 


.26982 


3.70616 


54 


7 


.21409 


4.05797 


.23301 


4.29159 


.25149 


3.97027 


.27013 


3.70188 


53 


8 


.21499 


4.05138 


.23332 


4.28595 


.25180 


3.97139 


.27044 


3.69761 


52 


9 


.215^9 


4.04480 


.23303 


4.28032 


.25211 


3.90051 


.27076 


3.69335 


51 


10 


.21500 


4.03825 


.23393 


4.27471 


.25242 


3.90165 


.27107 


3.68909 


50 


11 


.21590 


4.63171 


.23424 


4.26911 


' .25273 


3.95680 


.27138 


3.68485 


49 


12 


.21021 


4.62518 


.23455 


4.26352 


.25304 


3.95196 


.27169 


3.68061 


48 


13 


.21051 


4.61868 


.23485 


4.25795 


.25335 


3.94713 


.27201 


3.67638 


47 


14 


.21082 


4.61219 


.23510 


4.25239 


.25300 


3.94232 


.27232 


3.67217 


46 


15 


.21712 


4.00572 


.23547 


4.24685 


.25397 


3.93751 


.27203 


3.66796 


45 


i 16 


.21743 


4.59927 


.23578 


4.24132 


.25428 


3.93271 


.27294 


3.66376 


44 


|17 


.21773 


4.59283 


.23008 


4.23580 


.25459 


3.92793 


.27326 


3.65957 


43 


18 


.21804 


4.58041 


.23039 


4.23030 


.25490 


3.92316 


.27357 


3.65538 


42 


19 


.21834 


4.58001 


.23070 


4.22481 


.25521 


3.91839 


.27388 


3.65121 


41 


20 


.21864 


4.57363 


.23700 


4.21933 


.25552 


3.91364 


.27419 


3.64705 


40 


21 


.21895 


4.56726 


.23731 


4.21387 


.25583 


3.90890 


.27451 


3.64289 


39 


22 


.21925 


4.56091 


.23702 


4.20842 


.25014 


3.90417 


.27482 


3.63874 


38 


23 


.21956 


4.55458 


.23793 


4.20298 


.25045 


3.89945 


.27513 


3.0:3461 


37 


24 


.21986 


4.54826 


.23823 


4.19756 


.25076 


3.89474 


.27545 


3.03048 


36 


25 


.22017 


4.54196 


.23854 


4.19215 


.25707 


3.89004 


.27576 


3.02036 


35 


26 


.22047 


4.53568 


.23885 


4.18675 


.25738 


3.88536. 


.27007 


3.62224 


34 


27 


.22078 


4.52941 


.23910 


4.18137 


.25769 


3.88068 


.27038 


3.61814 


33 


28 


.22108 


4.52316 


.23940 


4.17600 


.25800 


3.87601 


.27070 


3.01405 


32 


29 


.22139 


4.51693 


.23977 


4.17064 


.25831 


3.87136 


.27701 


3.60990 


31 


30 


.22169 


4.51071 


.24008 


4.16530 


.25862 


3.86671 


.27732 


3 00588 


30 


31 


.22200 


4.50451 


.24039 


4.15997 


.25893 


3.86208 


.27704 


3.60181 


29 


32 


.22231 


4.49832 


.24009 


4.15465 


.25924 


3.85745 


.27795 


3.59775 


28 


33 


.22261 


4.49215 


.24100 


4.14934 


.25955 


3.85284 


.27826 


3.59370 


27 


34 


.22292 


4.48600 


.24131 


4.14405 


.25986 


3.84824 


.27858 


3.58900 


26 


35 


.22322 


4.47986 


.24102 


4.13877 


.26017 


3.84364 


.27889 


3.58502 


25 


36 


.22353 


4.47374 


.24193 


4.13350 


.26048 


3.83906 


.27921 


3.58100 


24 


37 


.22383 


4.46764 


.24223 


4.12825 


20079 


3.83449 


.27952 


3.57758 


23 


38 


.22414 


4.46155 


.21254 


4.12301 


.20110 


3.82992 


.27983 


3.57357 


22 


39 


.22444 


4.45548 


.24285 


4.11778 


.20141 


3.82537 


.28015 


3.50957 


n 


40 


.22475 


4-44942 


.24316 


4.11256 


.20172 


3.82083 


.28046 


3.56557 


20 


41 


.22505 


4.44338 


.24347 


4.10736 


.20203 


3.81630 


.28077 


3.56159 


19 


'.2 


.22536 


4.43735 


.24377 


4.10216 


.20235 


3.81177 


.28109 


3.55701 


18 


13 


.22567 


4.431:34 


.24408 


4.09699 


.20206 


3.80726 


.28140 


3.55304 


17 


44 


.22597 


4.42534 


.24439 


4.09182 


.20297 


3.80276 


.28172 


3.54908 


10 


45 .22028 


4.41936 


.24470 


4.08666 


.20328 


3.79827 


.28203 


3.54573 


15 


10 .22058 


4.41340 


.24501 


4.08152 


.20359 


3.79378 


.28234 


3.54179 


11 


•17 


.22689 


4.40745 


.24532 


4.07639 


.28390 


3.78931 


.28200 


3.53785 


13 


48 


.22719 


4.40152 


.24562 


4.07127 


.26421 


3.78485 


.28297 


3.53393 


12 


10 


.22750 


4.39560 


.2^1593 


4.06616 


.20452 


8.78040 


.2^329 


3.53001 


11 


50 


.22781 


4.38969 


.24024 


4.06107 


.20483 


3.77595 


.28360 


3.52609 


10 


51 


.22811 


4.3a381 


.24655 


4.05599 


.20515 


3.77152 


.28391 


3.52219 


9 


52 


.22842 


4.37793 


.24686 


4.05092 


.20546 


3.76709 


.28423 


3.51829 


8 


53 


.22(]72 


4.37207 


.24717 


4.04580 


.20577 


3.76268 


.284r>4 


3.51441 


7 


51 


.22903 


4.30023 


; .24747 


4.04081 


.2()008 


3.75828 


.28480 


3.51053 


6 


55 


.22o;m 


4.3G040 


, .24778 


4.03578 


.20039 


3.75388 


.28517 


3.50666 


5 


50 


.22904 


4.3r)4.-)9 


.24809 


4.03070 


.20070 


3.74950 


.28549 


3.50279 


4 


57 


.22995 


4.31879 


.218-10 


4.02574 


.20701 


3.74512 


.28580 


3.49894 


3 


58 


.23026 


4.34300 


.24871 


4.02074 


.20733 


3.74075 


.28012 


3.49509 


2 


59 


.23056 


4.33723 


.24902 


4.01576 


.20704 


3.73640 


.28043 


3.49125 


1 


CO 

/ 


.23087 
C-otang 


4.33148 


.24033 


4.01078 


.20795^ 


3.73205 


.28675 


3.48741 





Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


/ 


„0 


7R° 1 


! 75° 1 


74° 





490 



NATURAL TANGENTS AND COTANGENTS. 





16- 


17° 1 


18° 1 


19° 


/ 

60 


/ 


Tang 

.28675 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 
.344:33 


Cotang 


"o 


3.48741 


.30573 


3.27085 


.32492 


3.07768 


2.90421 


1 


.28706 


3.48.359 


.30605 


3.26745 


.32524 


3.07464 


.34465 


2.90147 


59 


2 


.28738 


3.47977 


.30637 


3.26406 


.32556 


3.07160 


.34498 


2.89873 


58 


3 


.28769 


3.47596 


.30669 


3.26067 


: .32588 


3.06857 


.34530 


2.89600 


57 


4 


.28800 


3.47216 


.30700 


3.25729 


i .32621 


3.06554 


.34563 


2.89327 


56 


5 


.28832 


3.46837 


.30732 


3.25392 


.32653 


3.06252 


.34596 


2.89055 


55 


6 


.28864 


3.46458 


.30764 


3.25055 


.32685 


3.05950 


.34628 


2.88783 


54 


7 


.28895 


3.46080 


.30796 


3.24719 


.32717 


3.05649 


.34661 


2.88511 


53 


8 


.28927 


3.45703 


.30828 


3.24383 


.32749 


3.05349 


.34693 


2.88240 


52 


9 


.28958 


3.45327 


.30860 


3.24049 


i .32782 


3.05049 


.34726 


2.87970 


51 


10 


.28990 


3.44951 


.30891 


3.23714 


1 .32814 


3.04749 


.34758 


2 87700 


50 


11 


.29021 


3.44576 


.30923 


3.23381 


.32846 


3.04450 


.34791 


2.87430 


49 


12 


.29053 


3.44202 


.30955 


3.23048 


.32878 


3.04152 


.34824 


2.87161 


48 


13 


.29084 


3.43829 


.30987 


3.22715 


.32911 


3.03854 


.34856 


2.86892 


47 


14 


.29116 


3.43456 


.31019 


3.22384 


.32943 


3.03556 


.34889 


2.86624 


46 


15 


.29147 


3.43084 


.31051 


3.22053 


.32975 


3.03260 


.34922 


2.86356 


45 


16 


.29179 


3.42713 


.31083 


3.21722 


.33007 


3.02963 


.34954 


2.80089 


44 


17 


.29210 


3.42343 


.31115 


3.21392 


.33040 


3.02e87 


.34987 


2.85822 


43 


18 


.29242 


3.41973 


.31147 


3.21063 


.33072 


3.02372 


.35020 


2.855.55 


42 


19 


.29274 


3.41604 


.31178 


3.20734 


.33104 


3.02077 


.35052 


2.85289 


41 


20 


.29305 


3.41236 


.31210 


3.20406 


.33136 


3.01783 


.35085 


2.85023 


40 


21 


.29337 


3.40869 


.31242 


3.20079 


.33169 


3.01489 


.35118 


2.84758 


39 


22 


.29368 


3.40502 


.31274 


3.19752 


.83201 


3.01196 


.35150 


2.84494 


38 


23 


.29400 


3.40136 


.31306 


3.19426 


.33233 


3.00903 


.35183 


2.84229 


37 


24 


.29432 


3.39771 


.31338 


3.19100 


.33266 


3.00611 


.35216 


2.83965 


36 


25 


.29463 


3.39406 


.31370 


3.18775 


.33298 


3.00319 


.35248 


2.83702 


35 


26 


.29495 


3.39042 


.31402 


3.18451 


.33330 


3.00028 


.35281 


2.83439 


34 


27 


.29526 


3.38679 


.31434 


3.18127 


.33363 


2.99738 


.35314 


2.83176 


33 


28 


.29558 


3.38317 


.31466 


3.17804 


.33395 


2.99447 


.35346 


2.82914 


32 


29 


.29590 


3.37955 


.31498 


3.17481 


.33427 


2.99158 


.35379 


2.82653 


31 


30 


.29621 


3.37594 


.31530 


3.17159 


.33460 


2.98868 


.35412 


2.82391 


30 


31 


.29653 


3.37234 


.31562 


3.16838 


.33492 


2.98580 


.35445 


2.82130 


29 


32 


.29685 


3.36875 


.31594 


3.16517 


.33524 


2.98292 


.35477 


2.81870 


28 


33 


.29716 


3.36516 


.31626 


3.16197 


.33557 


2.98004 


.35510 


2.81610 


27 


34 


.29748 


3.36158 


.31658 


3.15877 


.33589 


2.97717 


.35543 


2.81350 


26 


35 


.29780 


3.35800 


.31690 


3.15558 


.33621 


2.97430 


.35576 


2.81091 


25 


36 


.29811 


3.35443 


.31722 


3.15240 


.33654 


2.97144 


.35608 


2.80833 


24 


37 


.29843 


3.35087 


.31754 


3.14922 


.33686 


2.96858 


.35641 


2.80574 


23 


38 


.29875 


3.34732 


.31786 


3.14605 


.33718 


2.96573 


.35674 


2.80316 


22 


39 


.29906 


3.34377 


.31818 


3.14288 


.33751 


2.96288 


.35707 


2.80059 


21 


40 


.29938 


3.34023 


.31850 


3.13972 


.33783 


2.96004 


.35740 


2.79802 


20 


41 


.29970 


3.33670 


.31882 


3.13656 


.33816 


2.95721 


.35772 


2.79545 


19 


42 


.30001 


3.33317 


.31914 


3.13341 


.33848 


2.95437 


.35805 


2.79289 


18 


43 


.30033 


3.. 32965 


.31946 


3.13027 


.33881 


2.95155 


.35838 


2.79033 


17 


44 


.30065 


3.32614 


.31978 


3.12713 


.33913 


2.94872 


.35871 


2.78778 


16 


45 


.30097 


3.32264 


.32010 


3.12400 


.33945 


2.94591 


.35904 


2.78523 


15 


46 


.30128 


3.31914 


.32042 


3.12087 


.33978 


2.94309 


.35937 


2.78269 


11 


47 


.30160 


3.31565 


.32074 


3.11775 


.34010 


2.94028 


.35969 


2.78014 


13 


48 


.30192 


3.. 31216 


.32106 


3.11464 


.34043 


2.93748 


.36002 


2.77761 


12 


49 


.30224 


3.30868 


.32139 


3.11153 


.34075 


2.93468 


.36035 


2.77507 


11 


50 


.30255 


3.30521 


.32171 


3.10842 


.34108 


2.93189 


.36068 


2.77254 


10 


51 


.30287 


3.30174 


.32203 


3.10532 


.34140 


2.92910 


.30101 


2.77002 


9 


52 


.30319 


3.29829 


.32235 


3.10223 


.34173 


2.92632 


.36i;]4 


2.7'orr,o 


8 


53 


.30351 


3.29483 


.32267 


3.09914 


.34205 


2.92354 


.36167 


2.76198 


r- 


54 


.30382 


3.29139 


.32299 


3.09606 


.34238 


2.92076 


.36199 


2.7'6217 


6 


55 


.30414 


3.28795 


.32331 


3.09298 


.34270 


2.91799 


.36232 


2.75r06 


5 


56 


.30446 


3.28452 


.32363 


3.08991 


.34303 


2.91523 


.36265 


2.75746 


4 


57 


.30478 


3.28109 


.32396 


3.08685 


.31335 


2. 91 2-16 


.3()298 


2.754')6 


3 


58 


.30509 


3.27767 


.32428 


3.08379 


.34368 


2.90971 


.36331 


2.75216 


2 


59 


.30541 


3.27426 


.32460 


3.08073 


.34100 


2.9()(;96 


.36;:(;4 


2.7^'/:'j: 


1 


60 


.30573 
Cotang 


3.27085 


_. 32492 


3.07768 


.34133 


2.90421 


.3(5397 
Cotang 


2.7474r. 





/ 


Tang 


Cotang 


Tang 


C^otani^ 


Tang 


Tang 




73° 1 


72° 1 


ri° 1 


70° 



491 



NATURAL TANGENTS AND COTANGENTS. 



/ 

"o 


20° 


21° 


22° 


i 23° 


/ 
60 


Tang 


Cotang 


1 Tang 


Cotang 


Tang 
.40403 


1 Cotang 
2.47509 


Tang 


Cotang 


.36397 


2.74748 


..38:386 


2.60509 


.42447 


2.-35585 


1 


.36430 


2.74499 


.38420 


2.6028:3 


.40436 


2.47:302 


.42482 


2.35395 


59 


2 


.36463 


2.74251 


.:384.53 


2.60057 


.40470 


2.47095 


.42516 


2.35205 


58 


3 


.3&496 


2.74004 


1 .38487 


2.59831 


.40504 


2.46888 


.42551 


2.35015 


57 


4 


.36529 


2.73756 


I ..38520 


2.59606 


.40538 


2.46682 


.42585 


2.a4825 


56 


5 


.36562 


2.73509 


j .3a5,53 


2.59381 


.40572 


2.46476 


.42619 


2.34636 


55 


6 


.36595 


2.732G3 


i ..38587 


2.59156 


.40606 


2.46270 


.42654 


2.34447 


54 


7 


.36628 


2.73017 


1 .38620 


2.58932 


.40640 


2.46065 


.42688 


2.. 34258 


53 


8 


.36661 


2.72771 


: .38654 


2.58708 


.40674 


2.45860 


.42722 


2.. 34069 


52 


9 


.36694 


2.72526 


.38687 


2.58484 


.40707 


2.45655 


.42757 


2.. 3.3881 


51 


10 


.36727 


2.72281 


.38721 


2.58261 


.40741 


2.45451 


.42791 


2.33693 


50 


11 


.36760 


2.72036 


.38754 


2.58038 


.40775 


2.45246 


.42826 


2.33505 


49 


12 


.36793 


2.71792 


.38787 


2.57815 


.40809 


2.45043 


.42860 


2.:3.3317 


48 


13 


.36826 


2.71548 


.38821 


2.57593 


.40843 


2.44839 


.42894 


2.3.3130 


47 


14 


.36859 


2.71305 


! .38854 


2.. 57:37! 


.40877 


2.44636 


.42929 


2.. 32943 


46 


15 


.36892 


2.71002 


.38888 


2.57150 


.40911 


2.44433 


.42963 


2.32756 


45 


16 


.36925 


2.70819 


.38921 


2.56928 


.40945 


2.44230 


.42998 


2.. 32570 


44 


17 


.36958 


2.70.577 


..38955 


2.56707 


.40979 


2.44027 


.4.30.32 


2..32.3a3 


43 


18 


.36991 


2.70335 


.38988 


2.. 50487 


.41013 


2.4.3825 


.43067 


2.-32197 


42 


19 


.37024 


2.70094 


! .39022 


2.. 56266 


.41047 


2.43623 


.4.3101 


2.32012 


41 


20 


.37057 


2.69853 


1 .39055 


2.56046 


.41081 


2.43422 


.43136 


2.31826 


40 


21 


.37090 


2.69612 


' ..39089 


2.55827 


.41115 


2.4.3220 


.43170 


2.31641 


39 


22 


.37123 


2.69371 


■ .39122 


2.5.5608 


.41149 


2.4:3019 


.43205 


2.31456 


38 


23 


.37157 


2.69131 


! .391.56 


2.55.389 


.41183 


2.42819 


.4.32.39 


2.-31271 


37 


24 


.37190 


2.68892 


: .39190 


2.55170 


.41217 


2.42618 


.43274 


2.31086 


36 


25 


.37223 


2.68653 


.39223 


2.54952 


.41251 


2.42418 


.4.3308 


2.30902 


35 


26 


.37256 


2.68414 


.39257 


2.54734 


.41285 


2.42218 


.43343 


2.. 30718 


34 


27 


.37289 


2.G8175 


.39290 


2.. 54.516 


.41319 


2.42019 


.43378 


2.. 305.34 


33 


28 


.37322 


2.67937 


.39.324 


2.54299 


.413.53 


2.41819 


.43412 


2.:30351 


32 


29 


.37355 


2.67700 


..39:357 


2.54082 


.41387 


2.41620 


.43447 


2.30167 


31 


30 


.37388 


2.67462 


1 .39391 


2.53865 


.41421 


2.41421 


.43481 


2.29984 


30 


31 


.37422 


2.67225 


! ..39425 


2.. 5.3648 


.41455 


2.41223 


.43516 


2.29801 


29 


32 


.37455 


2.66989 


.39458 


2.53432 


.41490 


2.41025 


.435,50 


2.29619 


28 


33 


.37488 


2.66Vo2 


.39492 


2.5.3217 


.41524 


2.40827 


.4:3585 


2.29437 


27 


34 


.37521 


2.6G516 


..39526 


2.5:3001 


.41558 


2.40629 


.43620 


2.29254 


26 


35 


.37554 


2.66281 


..39559 


2.52786 


.41592 


2.401.32 


.4.3654 


2.29073 


25 


36 


.37588 


2.66046 


.39593 


2.. 52571 


.41626 


2.40235 


.43689 


2.28891 


24 


;3r 


.37621 


2.65811 


.39626 


2.. 52:357 


.41660 


2.40038 


.43724 


2.28710 


23 


33 


.37654 


2.65576 


i .39660 


2.52142 


.41694 


2.. 39841 


.4.3753 


2.28528 


22 


30 


.37687 


2.6.5.342 


..39694 


2.. 51929 


.41728 


2.39645 


.43793 


2.28348 


21 


^:o 


.37720 


2.65109 


.39727 


2.51715 


.41763 


2.39449 


.43828 


2.28167 


20 


41 


.37V54 


2.64875 


.39761 


2.51502 


.41797 


2.39253 


.43862 


2.27987 


19 


42 


.37787 


2.64642 


..39795 


2.51289 


.41831 


2..3-K)58 


.43897 


2.27806 


18 


43 


.37820 


2.64410 


.39829 


2.51076 i 


.41865 


2.. 38863 


.43932 


2.27626 


17 


44 


.37853 


2.64177 


.39862 


2.508(>4 


41899 


2.38668 


.43966 


2.27447 


16 


45 


.37887 


2.63945 


..39896 


2.50652 


.419.33 


2.38473 


.44001 


2.27267 


15 


46 


.37920 


2.63714 


.39930 


2.5O440 


.41968 


2.-38279 


.44036 


2.27088 


14 


47 


.379.53 


2. (mm 


..39963 


2.50229 i 


.42002 


2.. 38084 


.44071 


2.26909 


13 


48 


.37986 


2.63252 


..39997 


2.50018 


.42036 


2., 37891 


.44105 


2.26730 


12 


49 


.:38020 


2.6.3021 


.40031 


2.49807 


.42070 


2.. 37697 


.44140 


2.26.552 


11 


50 


.138053 


2.62791 


.40065 


2.49597 j 


.42105 


2.37504 


.44175 


2.26374 


10 


51 


.38086 


2.62.561 


' .40098 


2.49.386 


.421.39 


2.37311 


.44210 


2.26196 


9 


52 


.:38120 


2.62:3:32 


.401.32 


2.49177 , 


.42173 


2.. 371 18 


.44244 


2.26018 


8 


53 


.38153 


2.62103 


.40166 


2.48967 


.42207 


2.. 36925 


.44279 


2.2.5840 


7 


,^' 


.38186 


2.61874 


.40200 


2.487.58 ' 


.42242 


2.36733 


.44314 


2.2,5663 


6 


55 


.:iS220 


2.61646 


.40234 


2.48549 


.42276 


2.. 36541 


.44:349 


2.25486 


5 


56 


.382.53 


2.61418 


.40267 


2 48340 


.42310 


2.36349 


.44:384 


2.25309 


4 


57 


.38286 


2.61190 


.40301 


2.481:32 


.42345 


2.. 36158 


.44418 


2.2-5132 


3 


58 


.3a320 


2.60963 


.403.35 


2.47924 


.42379 


2.:35967 


.44453 


2.24956 


2 


59 


..m3,53 


2.()07.36 


.40:369 


2.47716 


.42413 


2.35776 


.44488 


2.;^780 


1 


GO 

/ 


.38386 ! 


2.60.509 


.40403 
Cotang 


2.47.509 
Tang 


.42447 
Cotang 


2..3.5.5a5 


.44523 


2.24604 




/ 


Cotang 1 


Tang 


Tang 


Cotang 


Tang 


69° 1 


6 


8° 


67° 1 


66° 1 



492 



NATURAL TANGENTS AND COTANGENTS. 



/ 

~0 


24° 


25° 


26° 


27° 1 


Tang 
.44523 


Cotang 


Tang 

.46631 


Cotang 


Tang 

.48773 


Cotang 


Tang 

.50953 


Cotang 


2.24604 


2.14451 


2.05030 


1.96261 


1 


.44558 


2.24428 


.46666 


2.14288 


.48809 


2.04879 


.50989 


1.96120 


2 


.44593 


2.24252 


.46702 


2.14125 


.48845 


2.04728 


.51026 


1.95979 


3 


.44627 


2.24077 


.46737 


2.13963 


.48881 


2.04577 


.51063 


1.95838 


4 


.44662 


2.23902 


.46772 


2.13801 


.48917 


2.04426 


.51099 


1.95698 


5 


.44697 


2.23727 


.46808 


2.13639 


.48953 


2.04276 


.51136 


1.95557 


6 


.44732 


2.23553 


.46843 


2.13477 


.48989 


2.04125 


.51173 


1.95417 


7 


.44767 


2.23378 


.46879 


2.13316 


.49026 


2.03975 


.51209 


1.95277 


8 


.44802 


2.23204 


.46914 


2.13154 


.49062 


2.03825 


.51246 


1.95137 


9 


.44837 


2.23030 


.46950 


2.12993 


.49098 


:^. 03675 


.51283 


1.94997 


10 


.44872 


2.22857 


.46985 


2.12832 


.49134 


2.03526 


.51319 


1.94858 


11 


.44907 


2.22683 


.47021 


2.12671 


.49170 


2.03376 


.51356 


1.94718 


12 


.44942 


2.22510 


.47056 


2.12511 


.49206 


2.03227 


.51393 


1.94579 


13 


.44977 


2.22337 


.47092 


2.12350 


.49242 


2.03078 


.51430 


1.94440 


14 


.45012 


2.22164 


.47128 


2.12190 


.49278 


2.02929 


.51467 


1.94301 


15 


.45047 


2.21992 


.47163 


2.12030 


.49315 


2.02780 


.51503 


1.94162 


16 


.45082 


2.21819 


.47199 


2.11871 


.49351 


2.02631 


.51540 


1.94023 


17 


.45117 


2.21647 


.47234 


2.11711 


.49387 


2.02483 


.51577 


1.93885 


18 


.45152 


2.21475 


.47270 


2.11552 


.49423 


2.02335 


.51614 


1.93746 


19 


.45187 


2.21304 


.47305 


2.11392 


.49459 


2.02187 


.51651 


1.93608 


20 


.45222 


2.21132 


.47341 


2.11233 


.49495 


2.02039 


.51688 


1.93470 


21 


.45257 


2.20961 


.47377 


2.11075 


.49532 


2.01891 


.51724 


1.93332 


22 


.45292 


2. 20790 


.47412 


2.10916 


.49568 


2.01743 


.51761 


1.93195 


23 


.45327 


2.20619 


.47448 


2.10758 


.49604 


2.01596 


.51798 


1.93057 


24 


.45362 


2.20449 


.47483 


2.10600 


.49640 


2.01449 


.51835 


1.92920 


25 


.45397 


2.20278 


.47'519 


2.10442 


.49677 


2.01302 


.51872 


1.92782 


26 


.45432 


2.20108 


.47555 


2.10284 


.49713 


2.01155 


.51909 


1.92645 


27 


.45467 


2.19938 


.47590 


2.10126 


.49749 


2.01008 


.51946 


1.92508 


28 


.45502 


2.19769 


.47626 


2.09969 


.49786 


2.00862 


.51983 


1.92371 


29 


.45538 


2.19599 


.47662 


2.09811 


.49822 


2.00715 


.52020 


1.92235 


30 


.45573 


2.19430 


.47698 


2.09654 


.49858 


2.00569 


.52057 


1.92098 


31 


.45608 


2.19261 


.47733 


2.09498 


.49894 


2.00423 


.52094 


1.91962 


32 


.45643 


2.19092 


.47769 


2.09341 


.49931 


2.00277 


.52131 


1.91826 


33 


.45678 


2.18923 


.47805 


2.09184 


.49967 


2.00131 


.52168 


1.91690 


34 


.45713 


2.18755 


.47840 


2.09028 


.50004 


1.99986 


.52205 


1.91554 


35 


.45748 


2.18587 


.47876 


2.08872 


.50040 


1.99841 


.52242 


1.91418 


36 


.45784 


2.18419 


.47912 


2.08716 


.50076 


1.99695 


.52279 


1.91282 


37 


.45819 


2.18251 


.47948 


2.08560 


.50113 


1.99550 


.52316 


1.91147 


38 


.45854 


2.18084 


.47984 


2.08405 


.50149 


1.99406 


.52353 


1.91012 


39 


.45889 


2.17916 


.48019 


2.08250 


.50185 


1.99261 


.52390 


1.90876 


40 


.45924 


2.17749 


.48055 


2.08094 


.50222 


1.99116 


.52427 


1.90741 


41 


.45960 


2.17582 


.48091 


2.07939 


.50258 


1.98972 


.52464 


1.9060? 


42 


.45995 


2.17416 


.48127 


2.07785 


.50295 


1.98828 


.52501 


1.90472 


43 


.46030 


2.17249 


.48163 


2.07'630 


.50331 


1.98684 


.52538 


1.90337 


44 


.46065 


2.17083 


.48198 


2.07476 


.50368 


1.98540 


.52575 


1.90203 


45 


.46101 


2.16917 


.48234 


2.07321 


.50404 


1.98396 


.52613 


1.90069 


46 


.46136 


2.16751 


.48270 


2.07167 


.50441 


1.98253 


.52650 


1.89935 


47 


.46171 


2.16585 


.48306 


2.07014 


.50477 


1.98110 


.52687 


1.8G801 


48 


.46206 


2.16420 


.48342 


2.06860 


.50514 


1.97966 


.52724 


1.89667 


49 


.40242 


2.16255 


.48378 


2.06706 


.50550 


1.97823 


.52761 


J. 89533 


50 


.46277 


2.16090 


.48414 


2.06553 


.50587 


1.97681 


.52798 


1.89400 


51 


.46312 


2.15925 


.48450 


2.06400 


.50623 


1.97538 


.52836 


1.8926b 


52 


.46348 


2.15760 


.48486 


2.06247 


.50660 


1.97'895 


.52873 


1.89133 


53 


.46383 


2.15596 


.48521 


2.06094 


.50696 


1.97253 


.52910 


1.89000 


54 


.46418 


2.15432 


.48557 


2.05942 


.50733 


1.97111 


.52947 


1.88867 


55 


.46454 


2.15268 


.48593 


2.05790 


.50769 


1.96969 


.52985 


1.88734 


56 


.46489 


2.15104 


.48629 


2.05637 


.50806 


1.96827 


.53022 


1.88602 


57 


.46525 


2.14940 


.48665 


2.05485 


.50813 


1.96685 


.58059 


1.88469 


58 


.46560 


2.14777 


.48701 


2.05333 


.50879 


1.965M 


.53096 


1.88337 


59 


.46595 


2.14614 


.48737 


2.05182 


, .50916 


1.96402 


.53134 


1.88205 


60 


.46631 


2.14451 


.48773 


2.05030 


' .50953 
Cotang 


1.96261 


.53171_ 


1.88073 


/ 


Cotang 


Tang 


Cotang 


Tang 


Tang 


Cotang 


Tang 


65° 1 


64» 1 


63° 1 


62° 1 



498 



NATURAL TANGENTS AND COTANGENTS. 





2S^ 


29° 


30° 


3i° 


60 


"o 


Tang 
.53171 


Cotang 

l.<S8(3r8 


i Tang 
.55431" 


Cotang 


T?ng 
.57735 


Cotang 1 


Tang 


Cotang 


1.80405 1 


1.7-3205 ! 


.60086 


1.66428 


1 


.53208 


1.87941 


.55469 


1.80281 


.57774 


1.73089 1 


.60126 


1.66318 


59 


2 


.53246 


1.87809 : 


1 .55507 


1.80158 


.57813 


1.72973 1 


.60165 


1.66209 


58 


3 


.5328:3 


1.87677 


. 55545 


1.80034 


.57851 


1.72857 I 


.60205 


1.66099 


57 


4 


.53320 


1.87546 


.55583 


1.79911 


.57890 


1.72741 1 


.60245 


1.65990 


56 


5 


.53358 


1.87415 


: .55621 


1.79788 


.57929 


1.72625 


.60284 


1.65881 


55 


6 


.5:31395 


1.87283 1 


1 .55659 


1.79665 


.57968 


1.72509 


.60324 


1.65772 


54 


7 


.53432 


1.87152 '■ 


.55697 


1.79542 


.58007 


1.72:393 


.60364 


1.65663 


53 


8 


.5:3470 


1.87021 1 


.55736 


1.79419 


.58046 


1.72278 


.60403 


1.65554 


52 


9 


.53507 


1.86891 1 


.5.5774 


1.79296 


.58085 


1.72163 


.60443 


1.65445 


51 


10 


.53545 


1.86760 


.55812 


1.79174 , 


.58124 


1.72047 


.60483 


1.65a37 


50 


n 


.53582 


1.86630 ! 


.55850 


1.79051 ' 


.58162 


1.71932 


.60522 


1.65228 


49 


12 


.53620 


1.86499 


1 .55888 


1.78929 


.58201 


1.71817 


.60562 


1.65120 


48 


13 


.53657 


1.86369 


j .55926 


1.78807 t 


..58240 


1.71702 


.60602 


1.65011 


47 


14 


.53694 


1.86239 


1 .55964 


1.78685 


.58279 


1.71588 


.60642 


1.64903 


46 


15 


.5:3732 


1.86109 


! .56003 


1.78563 


.58318 


1.71473 


.60681 


1.64795 


45 


1G» 


.5:3709 


1.8597'9 


' .56041 


1.78441 


.58357 


1.71358 


.60721 


1.64687 


44 


17 


.53807 


1.85850 ! 


i .56079 


1.78319 


.58396 


1.71244 


.60761 


1.64579 


43 


18 


.53^4 


1.85720 i 


1 .56117 


1.78198 


.58435 


1.71129 


.60801 


1.64471 


42 


19 


.53882 


1.85591 ' 


: .56156 


1.78077 


.58474 


1.71015 


.60841 


1.64363 


41 


20 


.53920 


1.85462 1 


.56194 


1.77955 


.58513 


1.70901 


.60881 


1.64256 


40 


21 


.53957 


1.85333 ' 


.56252 


1.77834 


> .58552 


1.70787 


.60921 


1.64148 


39 


22 


.53995 


1.85204 


.50270 


1.77713 


.58591 


1.70673 


.60960 


1.64041 


38 


23 


.54032 


1.85075 ; 


.56:309 


1.77592 


.58631 


1.70560 


.61000 


1.63934 


37 


24 


.54070 


1.84946 


.56^47 


1.77471 


.58670 


1.70446 


.61040 


1.63826 


36 


25 


.54107 


1.84818 


.56385 


1.77351 


.58709 


1.70332 


.61080 


1.63719 


35 


26 


.54145 


1.84689 


.56424 


1.77230 


. 587-48 


1.70219 


.61120 


1.63612 


U 


27 


.54183 


1.84561 1 


.56462 


1.77110 


.58787 


1.70106 


.61160 


1.63505 


33 


28 


.54220 


1.84433 


.56501 


1.76990 


.58826 


1.69992 


.61200 


1.63398 


32 


29 


.54258 


1.84305 


.56539 


1.76869 


.58865 


1.69879 


.61240 


1.63292 


31 


30 


.54296 


1.84177 


.56577 


1.76749 


.58905 


1.69766 


.61280 


1.63185 


30 


31 


.54333 


1.84049 


1 .56616 


1.76629 


.58944 


1.69653 


.61320 


1.63079 


29 


32 


.54371 


1.8:3922 


.56654 


1.76510 


: .5898:3 


1.69541 


.61360 


1.62972 


28 


33 


.54409 


l.a3794 


i .56693 


1.76390 


.59022 


1.69428 


.61400 


1.62866 


27 


34 


.54446 


1.83667 


i .56731 


1.76271 


.59061 


1.69316 


.61440 


1.62760 


26 


35 


.54484 


1.83540 ! 


' .567-69 


1.76151 


.59101 


1.69203 


.61480 


1.62654 


25 


36 


.54522 


1.83413 , 


1 .56808 


1.76032 


.59140 


1.69091 


.61520 


1.62548 


24 


37 


.54560 


1.83286 


! .56846 


1.75913 


i .59179 


1.68979 


.61561 


1.62442 


23 


38 


.54597 


1.83159 


! .56885 


1.75794 


.59218 


1.68866 


.61601 


1.62336 


22 


39 


.54635 


l.a30:33 


.56923 


1.75675 


.59258 


1.68754 


.61641 


1.62230 


21 


40 


.54673 


1.82906 


.56962 


1.75556 


.59297 


1.68643 


.61681 


1.62125 


20 


41 


.54711 


1.82780 


' .57000 


1.75437 


.59336 


1.68531 


.61721 


1.62019 


19 


42 


.54748 


1.82654 


, .57aS9 


1.75319 


, .59376 


1.68419 


.61761 


1.61914 


18 


43 


.54786 


1.82528 


; .57078 


1.75200 


' .59415 


1.68308 


.61801 


1.61808 


17 


44 


. .54824 
.54862 


1.82402 , 


.57116 


1.75082 


.59454 


1.68196 


.61842 


1.61703 


16 


45 


1.82276 


' .57155 


1.74964 


.59494 


1.68085 


.61882 


1.61598 


15 


46 


.54900 


1.82150 ! 


.57193 


1.74846 


1 .59533 


1.67974 


.61922 


1.61493 


14 


47 


.54938 


1.82025 


.57232 


1.74728 


.59573 


1.67863 


.61962 


1.61388 


13 


48 


.549i5 


1.81899 


.57271 


1.74610 


.59612 


1.67752 


.62003 


1.61283 


12 


49 


.55013 


1.81774 


.57309 


1.74492 


.59651 


1.67641 


.62043 


1.61179 


11 


50 


.55051 


1.81649 


, .57348 


1.74375 


.59691 


1.67530 


.62083 


1.61074 


10 


51 


.55089 


1.81524 


! .57:386 


1.74257 


.59730 


1.67419 


.62124 


1.60970 


9 


52 


.55127 


1.81399 


.57425 


1.74140 


.59770 


1.67309 


.62164 


1.60865 


8 


53 


.55165 


1.81274 


i .57464 


1.74022 


.59809 


1.67198 


.62204 


1.60761 


7 


M 


.55203 


1.81ir)0 


.57503 


1.73905 


.50849 


1.67088 


.62245 


1.60657 


6 


55 


.55241 


1.81025 


.57541 


1.7:3788 


.59888 


1.66978 


.62285 


1.60553 


5 


56 


.55279 


i.mm 


.57580 


1.73671 


.59928 


1.66867 


.62325 


1.60449 


4 


57 


.55317 


1.80777 '• 


1 .57619 


1.73.555 


.59967 


1.66757 


.62366 


1.60345 


3 


58 


.55355 


1.80653 


; .57657 


1.7:^:38 


.60007 


1.66647 


.62406 


1.60241 


2 


59 


.55393 


1.80529 


.57696 


1.73:321 


.60046 


1.66538 


.62446 


1.60137 


1 


60 


.554:31 


l.W)405 


; .577:35 


1.73205 i 


.60086 
Cotang 


1.66428 


_J52487 
Cotang 


1.60033 


_0 


Cotang 


Tang 


Cotang 
6 


Tang ! 
0" 


Tang 


Tang 


6V 


59° i 


58° 



494 



NATURAL TANGENTS AND COTANGENTS. 





32" li 


33° 1 


34° II 


35° 1 


/ 

60 


Tang 

.62487^ 


Cotang 1 


Tang 


Cotang 


Tang 


Cotang i 


Tang 

.7002f" 


Cotang 


1.60033 


.64941 


1.53986 


.67451 


1.48256 


1.42815 


1 


.62527 


1.59930 


.64982 


1.53888 


.67493 


1.48163 


.70064 


1.42726 


59 


2 


.62568 


1.59826 


.65024 


3.53791 


.67536 


1.48070 


. ?'0107 


1.42638 


58 


3 


.62608 


1.59723 


.65065 


1.53693 


.67578 


1.47977 : 


.70151 


1.42550 


57 


4 


.62649 


1.59620 


.65106 


1.53595 


.67620 


1.47885 


.70194 


1.42462 


56 


5 


.62689 


1.59517 


.65148 


1.53497 


.67663 


1.47792 


.70238 


1.42374 


55 


6 


.62730 


1.59414 


.65189 


1.53400 


.67705 


1.47699 


.70281 


1.42286 


54 


7 


.62770 


1.59311 


.65231 


1.53302 


.67748 


1.47607 


.70325 


1.42198 


53 


8 


.62811 


1.59208 


.65272 


1.53205 


.67790 


1.47514 


.703G8 


1.42110 


52 


9 


.62852 


1.59105 


.65314 


1.53107 


.67832 


1.47422 


.70412 


1.42022 


51 


10 


.62892 


1.59002 


.65355 


1.53010 


.67'87'5 


1.47330 


.70455 


1.41934 


50 


11 


.62933 


1.58900 


.65397 


1.52913 


.67917 


1.47238 


.70499 


1.41847 


49 


12 


.62973 


1.58797 


.65438 


1.52816 


.67960 


1.47146 


.70542 


1.41759 


48 


13 


.63014 


1.58695 


.65480 


1.52719 


.68002 


1.47053 


.70586 


1.41672 


47 


14 


.63055 


1.58593 


.65521 


1.52622 


.68045 


1.46962 


.70629 


1.41584 


40 


15 


.63095 


1.58490 


.65563 


1.52525 


.68088 


1.46870 


.70673 


1.41497 


45 


16 


.63136 


1.58388 


.65604 


1.52429 1 


.68130 


1.46778 


.70717 


1.41409 


44 


17 


.63177 


1.58286 


.65646 


1.52332 


.68173 


1.46686 


.70760 


1.41322 


43 


18 


.63217 


1.58184 


.65688 


1.52235 


.68215 


1.46595 


.70804 


1.41235 


42 


19 


.63258 


1.58083 


.65729 


1.52139 


.68258 


1.46503 


.70848 


1.41148 


41 


20 


.63299 


1.57981 


.65771 


1.52043 


.68301 


1.46411 


.70891 


1.41061 


40 


21 


.63340 


1.57879 


.65813 


1.51946 


.68343 


1.46320 


.70935 


1.40974 


39 


22 


.63380 


1.57778 


.65854 


1.51850 


.68386 


1.46229 


.70979 


1.40887 


38 


23 


.63421 


1.57676 


.65896 


1.51754 


.68429 


1.46137 


.71023 


1.40800 


37 


24 


.63462 


1.57575 


.65938 


1.51658 


.68471 


1.46046 


.71066 


1.40714 


36 


25 


.63503 


1.57474 


.65980 


1.51562 


.68514 


1.45955 


.71110 


1.40G27 


35 


26 


.63544 


1.57372 


.66021 


1.51466 


.68557 


1.45864 


.71154 


1.40540 


'M 


27 


.63584 


1.57271 


.66063 


1.51370 


.68600 


1.45773 


.71198 


1.40454 


33 


28 


.63625 


1.57170 


.66105 


1.53275 


.68642 


1.45682 


.71242 


1.40367 


32 


29 


.63666 


1.57069 


.66147 


1.51179 


.68685 


1.45592 


.71285 


1.40281 


31 


30 


.63707 


1.56969 


.66189 


1.51084 


.68728 


1.45501 


.71329 


1.40195 


30 


31 


.63748 


1.56868 


.66230 


1.50988 


.68771 


1.45410 


.71373 


1.40109 


29 


32 


.63789 


1.56767 


.66272 


1.50893 


.68814 


1.45320 


.71417 


1.40022 


28 


33 


.63830 


1.56667 


.66314 


1.50797 


.68857 


1.45229 


.71461 


1.39936 


27 


34 


.63871 


1.56566 


.66356 


1.50702 


.68900 


1.45139 


.71505 


1.39850 


26 


35 


.63912 


1.56466 


.66398 


1.50607 


.68942 


1.45049 


.71549 


1.39764 


25 


36 


.63953 


1.56366 


.66440 


1.50512 


.68985 


1.44958 


.71593 


1.39679 


24 


37 


.63994 


1.56265 


.66482 


1.50417 


.69028 


1.44868 


.71637 


1.39593 


23 


38 


.64035 


1.56165 


.66524 


1.50322 


.69071 


1.44778 


.71681 


1.39507 


22 


39 


.64076 


1.56065 


.66566 


1.50228 


.69114 


1.44688 


.71725 


1.39421 


21 


40 


.64117 


1.55966 


.66608 


1.50133 


.69157 


1.44598 


.71769 


1.39336 


20 


41 


.64158 


1.55866 


.66650 


1.50038 


.69200 


1.44508 


.71-813 


1.39250 


19 


42 


.64199 


1.55766 


.66692 


1.49944 


.69243 


1.44418 


.71857 


1.39165 


18 


43 


.64240 


1.55666 


.667'34 


1.49849 


.69286 


1.44329 


.71901 


1.39079 


17 


44 


.64281 


1.55567 


.66776 


1.49755 


.69329 


1.44239 


.71946 


1.38994 


16 


45 


.64322 


1.55467 


.66818 


1.49661 


.69372 


1.44149 


.71990 


1.38909 


15 


46 


.64363 


1.55368 


.66860 


1.49566 


.69416 


1.44060 


.72034 


1.38824 


14 


47 


.64404 


1.55269 


.66902 


1.49472 


.69459 


1.43970 


.72078 


1.38738 


13 


48 


.64446 


1.55170 


.66944 


1.49378 


.69502 


1.43881 


.72122 


1.38053 


12 


49 


.64487 


1.55071 


.66986 


1.49284 


.69545 


1.43792 


.72167 


1.385C8 


11 


50 


.64528 


1.54972 


.67028 


1.49190 


.69588 


1.43703 


.72211 


1.38-184 


10 


51 


.64569 


1.54873 


.67071 


1.49097 


.69631 


1.43614 


.72255 


1.3a399 


9 


52 


.64610 


1.54774 


,67113 


1.49003 


.69675 


1.43525 


.72299 


1.38314 


8 


r>3 


.64652 


1.54675 


; .67155 


1.48909 


.69718 


1.43436 


.72344 


1.38;?C9 


7 


54 


.64693 


1.54576 


.67197 


1.48816 


.69761 


1.43347 


.72388 


1.38145 


6 


55 


.64734 


1.54478 


.67239 


1.48722 


.69804 


1.43258 


.72432 


1.38060 


5 


56 


.64775 


1.54379 


.67282 


1.48629 


.69847 


1.43169 


.72-177 


1.37976 


4 


5? 


.64817 


1.54281 


.67324 


1.48536 


.69891 


1.43080 


.72521 


1.37891 


3 


5F 


.64858 


1.54183 


.67366 


1.48442 


.69934 


1.42992 


.72565 


1.37807 


2 


5C 


1 .64899 


1.54085 


.67409 


1.48349 


.69977 


1.42903 


.72610 


1.37722 


1 


C- 


) .6^4941 


1.53986 


, .67451 


1.48256 


.7(X)21 


1.42815 


.72654 


1.37638 




f 

1 


/ 


Cotang 


Tang 


Cotang 


Tang 


I Cotang 


Tang 


Cotang 


Tang 


_ 


57° 


56° 


55° 


i 54° 



m 



NATURAL TAXGi^JNTS AND COTANGENTS. 





36° i 


37° 


38° 1 


39° 


/ 
60 


'1 


Tang 1 


Cotang 


. 75355 


Cotang 
1.32704 


Tang ! 
.78129 


Cotang 


Tang Cotang 
.80978 1.2^^490 i 





.72654 1 


1.37638 


1.27994 


1 


.72699 


1.37554 : 


.75401 


1.32624 


.78175 


1.27917 


.81027 


1.23416 


59 


2 


.72743 


1.37470 i 


.75447 


1.32544 


.78222 


1.27841 


.81075 


1.23343 


58 


G 


.72788 


1.37386 1 


.75492 


1.32464 


.78269 


1.27764 


.81123 


1.23270 


57 


4 


.72832 


1.37302 


.75538 


1.32384 


.78316 


1.27688 


.81171 


1.23196 


56 


5 


.72877 


1.37218 1 


.75584 


1.32304 


.78363 


1.27611 


.81220 


1.23123 


55 


6 


.72921 


1.371:34 


.75629 


1.32224 


.78410 


1.27535 


.81268 


1.23050 


54 


7 


.72966 


1.37050 


.75675 


1.32144 


.78457 


1.27458 


.81316 


1.22977 


53 


8 


.73010 


1.36967 , 


.75721 


1.32064 


.78504 


1.27382 


.81364 


1.22904 


52 


9 


.73055 


1.36883 1 


.75767 


1.31984 


.78551 


1.27306 


.81413 


1.22831 


51 


10 


.73100 


1.36800 1 


.75812 


1.31904 


.78598 


1.27230 


.81461 


1.22758 


50 


11 


.73144 


1.36716 ' 


.75858 


1.31825 


.78645 


1.27153 


.81510 


1.22685 


49 


12 


.73189 ' 


1.36633 i 


.75904 1.31745 


.78692 


1.27077 ! 


.81558 


1.22612 


48 


13 1 


.73234 


1.36549 


.75950 


1.31666 


.78739 


1.27001 


.81606 


1.22539 


47 


14' 


.73278 


1.36466 


.75996 


1.31586 


.78786 


1.26925 


.81655 


1.22467 


46 


15 i 


.73323 


1.36383 


.76042 


1.31507 


.78834 


1.26849 


.81703 


1.22394 


45 


16 


.73368 


1.36300 


.76088 


1.31427 


.78881 


1.26774 1 


.81752 


1.22321 


44 


17 


.73413 


1.36217 


.76134 


1.31348 


.78928 


1.26698 ! 


.81800 


1.22249 


43 


18 


.73457 


1.36134 


.76180 


1.31269 


.78975 


1.26622 


.81849 


1.22176 


42 


19 


.73502 


1.36051 


.76226 


1.31190 


.79022 


1.26546 


.81898 


1.22104 


41 


20 


.73547 


1.35968 1 


.76272 


1.31110 1 


.79070 


1.26471 


.81946 


1.22031 


40 


21 


.73592 


1.35885 ' 


.76318 


1.31031 ' 


.79117 


1.26395 


.81995 


1.21959 


39 


22 


.73637 


1.35802 


.76364 


1.30952 i 


.79164 


1.26319 1 


.82044 


1.21886 


38 


23 


.73681 


1.35719 


.76410 


1.30873 


.79212 


1.26244 ' 


.82092 


1.21814 


37 


24 


.73726 


1.35637 


.76456 


1.30795 


.79259 


1.26169 


.82141 


1.21742 


36 


25 


.73771 


1.35554 1 


.76502 


1.30716 


.79306 


1.26093 


.82190 


1.21670 


35 


26 


.73816 


1.35472 1 


.76548 


1.30637 


.79354 


1.26018 


.82238 


1.21598 


34 


27 


.73861 


1.35389 


.76594 


1.30558 


.79401 


1.25943 


.82287 


1.21526 


33 


28 


.73906 


1.35307 


.76640 


1.30480 


.79449 


1.25867 


.82336 


1.21454 


32 


29 


.73951 


1.35224 


.76686 


1.30401 


.79496 


1.25792 


.82385 


1.21382 


31 


30 


.73996 


1.35142 


.76733 


1.30323 


.79544 


1.25717 


.82434 


1.21310 


30 


31 


.74041 


1.35060 


.76779 


1.30244 


.79591 


1.25642 


.82483 


1.21238 


29 


32 


.74086 


1.34978 i 


.76825 


1.30166 


.79639 


1.25567 


.82531 


1.21166 


28 


33 


.74131 


1.34896 : 


.76871 


1.30087 


.79686 


1.25492 


.82580 


1.21094 


27 


M 


.74176 


1.34814 1 


.76918 


1.30009 


.79734 


1.25417 


.82629 


1.21023 


26 


35 


.74221 


1.34732 ' 


.76964 


1.20931 


.79781 


1.25343 


.82678 


1.20951 


25 


36 


.74267 


1.34650 


.77010 


1.29853 


.79829 


1.25268 


.82727 


1.20879 


24 


37 


.74312 


1.34568 


.77057 


1.29775 


.79877 


1.25193 


.82776 


1.20808 


23 


38 


.74357 


1.34487 


.77103 


1.29696 


.79924 


1.25118 


.82825 


1.20736 


22 


39 


.74402 


1.34405 


.77149 


1.29618 


! .79972 


1.25044 


.82874 


1.20665 


21 


40 


.74447 


1.34323 


.77196 


1.29541 


.80020 


1.24969 


.82923 


1.20593 


20 


41 


.74492 


1.34242 


.77242 


1.29463 


.80067 


1.24895 


.82972 


1.20522 


19 


42 


.74538 


1.34160 


.77289 


1.29385 


.80115 


1.24820 


.83022 


1.20451 


18 


43 


.74583 


1.34079 


.77335 


1.29307 


.80163 


1.24746 


.83071 


1.20379 


17 


44 


.74628 


1.33998 


.77382 


1.29229 


.80211 


1.24672 


.83120 


1.20308 


16 


45 


.74674 


l.a3916 


.77428 


1.29152 


.80258 


1.24597 


.83169 


1.20237 


15 


46 


.74719 


1.33835 


. 77475 


1.29074 


.80306 


1.24523 


.83218 


1.20166 


14 


47 


.74764 


1.33754 


.77521 


1.28997 


.80354 


1.24449 


.83268 


1.20095 


13 


48 


.74810 


1.33673 


.77568 


1.28919 


i .80402 


1.24:375 


.83317 


1.20024 


12 


49 


.74855 


1.33592 


.77615 


1.28842 


.80450 


1.24:301 


.83366 


1 . 19953 


11 


50 


.74900 


l.:^ll 


.77661 


1.28764 


.80498 


1.24227 


.83415 


1.19882 


10 


51 


.74946 


l.a3430 


.77708 


1.28687 


.80546 


1.24153 


.83465 


1.19811 


9 


52 


.74991 


l.:3:i349 


.ViiiA 


1.28610 


.80594 


1.24079 


.83514 


1.19740 


8 


53 


.75037 


1. .33268 


.77801 


1.285:33 


.80642 


1.24005 


.83564 


1.19669 


7 


54 


.75082 


1.3.3187 


.77848 


1.28456 


.80690 


1.23931 


.83613 


1.19599 


6 


55 


.75128 


1.33107 


.77895 


1.28:379 


.807:38 


1.23858 


.a3662 


1.19528 


5 


56 


.75173 


i.;3:3026 


.77941 


1.28302 


.80786 


1.23784 


.83712 


1.19457 


4 


57 


.75219 


1.32946 


.77988 


1.28225 


.808:34 


1.2:3710 


.83761 


1.19387 


3 


58 


.75264 


1.32865 


.78035 


1.28148 


.80882 


1.23637 


.83811 


1.19316 


2 


59 


.75:^10 


1.32785 


.7S0H2 


1.28071 


.809:30 


1.2:3563 


.83860 


1 . 19246 


1 


60 


.75:i55 
Cotang 


1.32704 


i .78129 


1.27994 


.80978 


1.23490 


.83910 


1.19175 





Tang 


Cotang 


Tang 


Cotang 


j Tang 


Cotang 


1 Tang 


/ 


1 53° 


52° 


51° 


i 50° 





496 



Natural tangents and cotangents. 



/ 

"o 


40<^ 


41° ! 


42° 


43° 1 


60 


Taiig" f Cotang 


Tang 

.86929" 


Cotang 


Tang 1 Cotang 


Tang i Cotang- 


.83910 


1.19175 


1.15037 


.90040 


1.11061 


.93252 


1.07237 


1 


.83960 


1.19105 


.86980 


1.14969 


.90093 


1.10996 


.93306 


1.07174 


59 


2 


.84009 


1.19035 


.87031 


1.14902 


.90146 


1.10931 


.93360 


1.07112 


58 


3 


.84059 


1.18964 


.87082 


1.14834 


.90199 


1.10867 


.93415 


1.07049 


57 


4 


.84108 


1.18894 


.87133 


1.14767 


.90251 


1.10802 


.93469 


1.06987 


56 


5 


.84158 


1.18824 


.87184 


1.14699 


.90304 


1.10737 


.93524 


1.06925 


55 


6 


.84208 


1.18754 


.87236 


1.14632 


.90357 


1.10672 


.93578 


1.00862 


54 


7 


.84258 


1.18684 


.87287 


1.14565 


.90410 


1.10607 


.93633 


1.00800 


53 


8 


.84307 


1.18614 


.87338 


1.14498 


.90463 


1.10543 


.93688 


1.06738 


52 


9 


.84357 


1.18544 


.87389 


1.14430 


.90516 


1.10478 


.93742 


1.06676 


51 


10 


.84407 


1.18474 


.87441 


1.14363 


.90569 


1.10414 


.93797 


1.06613 


50 


11 


.84457 


1.18404 


.87492 


1.14296 


.90621 


1.10349 


.93852 


1.06551 


49 


12 


.84507 


1.18334 


.87543 


1.14229 


.90674 


1.10285 


.93906 


1.06489 


48 


13 


.84556 


1.18264 


.87595 


1.14162 


.90727 


1.10220 


.93961 


1.06427 


47' 


14 


.84606 


1.18194 


.87646 


1.14095 


.90781 


1.10156 


.94016 


1.063G5 


4G 


15 


.84656 


1.18125 


.87698 


1.14028 


.90834 


1.10091 


.94071 


1.06303 


45 


16 


.84706 


1.18055 


.87749 


1.13961 


.90887 


1.10027 


.94125 


1.06241 


44 


17 


.84756 


1.17986 


.87801 


1.13894 


.90940 


1.099G3 


.94180 


1.06179 


43 


18 


.84806 


1.17916 


.87852 


1.13828 


.90993 


1.09899 


.94235 


1.06117 


42 


19 


.84856 


1.17846 


.87904 


1.13761 


.91046 


1.09834 


.942C0 


1.0G056 


41 


20 


.84906 


1.17777 


.87955 


1.13694 


.91099 


1.09770 


.94345 


1.05994 


40 


21 


.84956 


1.17708 


.88007 


1.13627 


.91153 


1.09706 


.94400 


1.05932 


39 


22 


.85006 


1.17638 


.88059 


1.13561 


.91206 


1.09642 


.94455 


1.05870 


38 


23 


.85057 


M7569 


.88110 


1.13494 


.91259 


1.09578 


.94510 


1.05809 


37 


24 


.85107 


1.17500 


.88162 


1.13428 


.91313 


1.09514 


.94565 


1.05747 


36 


25 


.85157 


1.17430 


.88214 


1.13361 


.91306 


1.09450 


.94620 


1.05685 


35 


26 


.85207 


1.17361 


.88265 


1.13295 


.91419 


1.09386 


.94676 


1.05624 


34 


27 


.85257 


1.17292 


.88317 


1.13228 


.91473 


1.09322 


.94731 


1.05562 


33 


28 


.85308 


1.17223 


.88369 


1.13162 


.91526 


1.09258 


.94786 


1.05501 


32 


29 


.85358 


1.17154 


.88421 


1.13096 


.91580 


1.09195 


.94841 


1.05439 


31 


30 


.85408 


1.17085 


.88473 


1.13029 


.91633 


1.09131 


.94896 


1.05378 


30 


31 


.85458 


1.17016 


.88524 


1.12963 


.91687 


1.09067 


.94952 


1.05317 


29 


32 


.85509 


1.16947 


.88576 


1.12897 


.91740 


1.09003 


.95007 


1.05255 


28 


33 


.85559 


1.16878 


.88628 


1.12831 


.91794 


1.08940 


.95062 


1.05194 


27 


34 


.85609 


1.16809 


.88680 


1.12765 


.91847 


1.08876 


.95118 


1.05133 


26 


35 


.85660 


1.16741 


.88732 


1.12699 


.91901 


1.08813 


.95173 


1.05072 


25 


36 


.85710 


1.16672 


.88784 


1.12633 


.91955 


1.08749 


.95229 


1.05010 


24 


37 


.85761 


1.16603 


.88836 


1.12567 


.92008 


1.08686 


.95284 


1.04949 


23 


38 


.85811 


1.16535 


.88888 


1.12501 


.92062 


1.08622 


.95340 


1.04888 


22 


39 


.85862 


1.16466 


.88940 


1.12435 


.92116 


1.08559 


.95395 


1.04827 


21 


40 


.85912 


1.16398 


.88992 


1.12369 


.92170 


1.08496 


.95451 


1.04766 


20 


41 


.85963 


1.16329 


.89045 


1.12303 


.92224 


1.08432 


.95506 


1.04705 


19 


42 


.86014 


1.16261 


.89097 


1.12238 


.92277 


1.08369 


.95562 


1.04644 


18 


43 


.86064 


1.16192 


.89149 


1.12172 


.92331 


1.08306 


.95618 


1.04583 


17 


44 


.86115 


1.16124 


.89201 


1.12106 


.92385 


1.08243 


.95673 


1.04522 


16 


45 


.86166 


1.16056 


.89253 


1.12041 


.92439 


1.08179 


.95729 


1.04461 


15 


46 


.86216 


1.15987 


.89306 


1.11975 


.92493 


1.08116 


.95785 


1.04401 


14 


47 


.86267 


1.15919 


.89358 


1.11909 


.92547 


1.08053 


.95841 


1.04340 


13 


48 


.86318 


1.15851 


.89410 


1.11844 


.92601 


1 .07990 


.95897 


1.CH279 


12 


49 


.86368 


1.15783 


.89463 


1 11778 


.92655 


1.07927 


.95952 


1.01218 


11 


50 


.86419 


1.15715 


.89515 


1.11713 


.92709 


1.07864 


.96008 


1.04158 


10 


51 


.86470 


1.15647 


.89567 


1.11648 


.92763 


1.07801 


.96064 


1.04097 


9 


52 


.86521 


1 . 15579 


.89620 


1.11582 


.92817 


1.07738 


.96120 


1.04036 


8 


' 53 


.86572 


1.15511 


.89672 


1.11517 


.92872 


1.07676 


.96176 


1.03976 


7 


54 


.86623 


1.15443 


.89725 


1.11452 


.92926 


1.07613 


.96232 


1.03915 


6 


55 


.8667'4 


1.15375 


.89777 


1.11387 


.92980 


1.07550 


.96288 


1.03855 


5 


56 


.86725 


1.15308 


.89830 


1.11321 


1 .98034 


1.07'487 


.96344 


1.03794 


4 


57 


.86776 


1.15240 


.89883 


1.11256 


1 .93088 


1. 07425 


.96400 


1.03734 


3 


58 


.86827 


1.15172 


.89935 


1.11191 


.93143 


1.07362 


.96457 


1.03674 


2 


59 


.86878 


1.15104 


.89988 


1.11126 


.93197 


1.07299 


.96513 


1.03613 


1 


60 

/ 


.86929 


1.15037 


.90040 


1.11061 


.93252 


1.07237 


.96569 
Cotang 


1.035.53 





Cotarif^ 


1 Tang 


Co tang 1 Tang 
1 48° 


Cotang 


Tang 


'Jang 


' 


4 


t9- 


4 


7° 


i . 4 


6° 





497 



Natural tangents and cotangents. 



/ 


440 


'- 


i ' 
20 


1 440 


1 
1 , 


40 


440 






Tang 1 Cotang 


Tang 


Cotang 




Tang 


Cotang 







.96569 j 1.03553 i 60 


.97700 


1.02355 j40 


.98843 


1.01170 


20 


1 


.96625 ! 1.03193 


59 


21 


.97756 


1.02295 39 


141 


.98901 


1.01112 


19 


2 


.96681 1.0;ii:^ 


58 


22 


.97813 


1.022:36 


m 


42 


.98958 


1.01053 


18 


3 


.96738 1.03372 


57 


23 


.97870 ! 1.02176 


37 


43 


.99016 


1.00994 


17 


4 


.96794 1 1.03312 1 56 1 


24 


.97927 


1.02117 


36 


44 


.99073 


1.00935 


16 


5 


.96850 ! 1.03252 


55 


25 


.979a4 


1.02057 


35 


45 


.99131 


1.00876 


15 


6 


.96907 1 1.03192 


54 


26 


.98041 


1.01998 


34 


l46 


.99189 


1.00818 


14 


7 


.96963 i 1.03132 


53 


27 


.98098 


1.019:39 j33 


147 


.99247 


1.00759 


13 


8 


.97020 : 1.03072 


52 


28 


.98155 


1.01879 32 


I48 


.99304 


1.00701 


12 


9 


.97076 ! 1.03012 


51 


29 


.98213 


1.01820 


31 


I49 


.99362 


1.00642 


11 


10 


.9713:3 ; 1.02952 


50 


30 


.98270 


1.01761 


30 


50 


.99420 


1.00583 


10 


11 


.97189 


1.02892 


49 


31 


.98327 


1.01702 


29 


51 


.99478 


1.00525 


9 


12 


.97246 


1.02832 


48 


32 


.98384 


1.01642 


28 


52 


.99536 


1.00467 


8 


13 


.97302 


1.02772 


47 


33 


.98441 


1.01583 27! 


53 


.99594 


1.00408 


7 


14 


.97359 


1.02713 


46 


34 


.98199 


1.01524 i26i 


54 


.99652 


1.00350 


6 


15 


.97416 i 1.02653 


45 


35 


.98556 


1.01465 25 


55 


.99710 


1.00291 


5 


16 


.97472 , 1.02593 


44 


36 


.98613 


1.01406 24 


56 


.99768 


1.00233 


4 


17 


.97529 1 1.02533 


43 


37 


.98671 


1.01347 23 


57 


.99826 


1.00175 


3 


18 


.97586 1.02474 


42 


38 


.98728 


1.01288 221 


58 


.99884 


1.00116 


2 


19 


.97643 1.02414 


41 


39 


.98786 


1.01229 i21| 


59 


.99942 


1.00058 


1 


20 


.97700 1.0':^355 


40 


40 

/ 


.98843 


1.01170 20 


60 

/ 


1.00000 


1.00000 





/ 


Cotang i Tang 


/ 


Cotang Tang 


/ 


Cotang Tang 


/ 




45° 


45° 


45° 





498 



DEFmiTlONS OF TERMS USED. 499 



Definitions of Terms used In Construction, 

Altars : The steps on the sides and ends of a dry -dock. 

Apron : A covering of stone, timber, or metal to protect a sur- 
face against the action of water flowing over it. 

Aqjeduct : A conduit for the conveyance of water. More 
particularly applied to those of considerable magnitude intended 
to supply cities with water derived from a distance for domestic 
purposes, or for conveying the w^ater of canals across rivers or 
valleys. 

Arris : The edge in which two surfaces meet; the intersection 
of two planes. 

Ballast : Broken stone or gravel on which railroad cross- ties 
are laid. 

Base : Lower portion of a post or column, but is generally used 
to designate the lowest portion of any structure. 

Basil : The angle at the cutting edge of a tool or instrument. 

Battlement; A notched or indented parapet, of which the 
higher parts are called merlonSy and the openiugs or lower por- 
tions embrasures or loops. 

Beam (see Girder) : A '* spandrel-beam" is a common term for 
a steel or iron beam carrying a portion of the exterior wall of a 
building. 

Bearing: The span or length in the clear between the points 
of support of a beam, etc. The points of support themselves of 
a beam, etc. 

Bearing- plate . A plate of cast or wrought iron placed on a 
wall to support the ends of beams, etc. 

Bearing- STRESS : The stress which occurs when one body 
presses against another so as to tend to produce indentation or 
cutting. 

Bed-plate : A large plate of iron laid on a foundation for 
something to rest on. 

Beetle : A heavy wooden rammer. 

Behmio : (1) The embankment of a canal, opposite to and like 
the tow-path; (2) tlie space between the toe of an eihibankment 
slone and tlie edge of a ditch. 

\lKVK\i : A term for a jiImiic having any other angle than 45° or 
i/0'' formed l)y cutting olf the sharp edge, as of a board. 



dOO definitions of Terms used. 

BlocS^ : A grooved pulley, rotating on a pintle and mounted 
in a casing called a sliell, which is furnished with a hook, eye, or 
strap by which it may be attached to an object. They are used 
extensively for moving heavy weights. Blocks are of various 
forms, each having a particular name: Single or Double Block, 
Differential Block, Fall-block, Purchase-block, Snatch-block, Stand- 
ing Block, Tail-block, etc. 

Block and Tackle : A term including the block and the rope 
rove through it, for hoisting or obtaining a purchase. 

Blockings : Pieces of timber used to raise barrels, etc., off the 
ground. 

Bolster : The resting-place of a truss-bridge on its pier or 
abutment, or a timber or thick iron plate placed between the end 
of a bridge and its seat on the abutment. 

Boning, in carpentry and masonry, is performed by placing 
two straight-edges on an object and sighting on their upper edges 
to see if they range. If they do not, the surface is said to be in 
wind. 

Bore • The inner diameter of a pipe, hollow cylinder, etc. 

Bouiiow-riT : A pit dug in order to obtain material for an em- 
bankment. 

Boulder : A stone rounded by natural attrition ; a rounded 
mass of rock transported from its original bed. 

Break Joint : So to overlap pieces that the joints shall not be 
in line. 

Breaking Load ; The load or w'eight which will just produce 
fracture in a piece of material or structure. 

Breakwater : A structure of stone or timber so placed as to 
break the force of the waves to protect an anchorage or harbor. 

Breast-w^all : One built to prevent the falling of a vertical 
face cut into the natural soil. 

Bkidge-truss •. A structure of thrust- and tension-pieces, form- 
ing a skeleton beam. It has several varieties. 

Brittleness : The inclination of a material to break sudden- 
ly under any stress. 

Bulkhead : A timber or other structure built along the sides 
of streams or rivers. The face of a wharf parallel to the stream. 

Butt : The name given to an ordinary door-hinge. 

Calibre : The inner diameter or bore of pipes, etc. 

Calipers : Compasses or dividers with curved legs for meas- 
uria:r (nitside and inside diameters. 



defi:n^itions of terms used. 501 

Calk or Caulk ; To fill seams or joints with something to pre 
vent leaking. 

Camber : A slight upward curve given to a beam or truss to^ 
allow for settling. 

Cant-hook : A lever and suspended hook for turning logs. 

Cantilever : A projecting beam or bracket which, however 
it may be loaded, has the upper fibres in tension and the lower 
in compression. A bridge formed by projecting brackets which 
support a central portion. 

Causeway : A raised footway or roadway. 

Chairs : Castings used to support the ends of rails or timbers. 

Chamfer means much the same as bevel, but applies more 
especially when two edges are cut away so as to form either a 
chamfer groove or a projecting sharp edge. 

Chipping-chisel : A cold-chisel with a slightly convex face 
and an angle of about 80°. 

Chipping-piece : The projecting piece left on a forged surface, 
affording surplus metal for reduction to a line wdth the chipping- 
chisel. 

The projecting piece of iron cast on the face of a piece of 
iron framing where it is intended to be fitted against another. 

Chock : Any piece used for filling up a chance hole or va- 
cancy. 

Clearing : Catting down timber and brush. 

Clevis : See Shackle. 

Compression is the stress produced by pressure; it shortens 
the material to which it is applied and tends to cause rupture by 
crushing. 

Corbel ; A horizontal projecting piece which assists in sup- 
porting one resting upon it which projects still farther. 

Counterbrace : The member of a truss which is designed to 
resist both tensile and compressive strains. 

Countersink. — An enlargement of a hole to receive the head 
of a bolt, screw, rivet, etc. The sides of the hole are merely 
chamfered when it is to receive the head of an ordinary wood- 
screw. When a flat-head^ screw or bolt-head is to be let in 
flush with the surface a flat bottom is required. 

Covering-stones : In culverts the large stones extending 
across Ihe top from side to side and resting upon the walls. 

Crab : A winch on a movable frame with power gearing, used 
in connection with derricks and other non-permanent hoisting- 
machines. 



502 DEFINITIOKS OF TERMS USED. 

Cradle : Applied to various kinds of timber supports which 
partly enclose the mass sustained. The masonry built around 
and below the haunches of an arch in sewers 

Crane ; A machine for hoisting and lowering heavy weights. 

Crest : The top part of a dam over which the water flows. 

Crest RAILING : The railing surmounting the ridge of the 
roof of a building. 

Cross- STRAIN : See Transverse Stress. 

Crowbar : A bar of iron used as a lever for various purposes, 
often pointed at one end. 

Curb : 1. A stone, timber, or iron structure formed inside a 
well to keep back the surrounding earth. 2. A broad, flat, 
circular ring of timber or iron placed under the bottoms of 
circular walls in wells, shafts, etc., to prevent unequal settle- 
ment. 3. The stones dividing the sidewalk from the carriage- 
way of streets. 

Culvert : A waterway or drain of masonry or earthenware or 
iron pipe beneath a road or canal. 

Culled : Assorted, picked out, selected. 

CuRTAiN-WALL is that part of the exterior walls of buildings 
extending from the line of the window-cap of one story to the 
line of the window-sill of the next story above. 

Cutwater or Starling : The projecting ends of a bridge- 
pier, etc., usually so shaped as to allow water, ice, etc., to strike 
them with but little injury. 

Dam : A bank of earth or a structure of stone, timber, etc., 
constructed across a stream to store water. 

Dead Load : A load applied gradually and steadily. 

Deadman : A log of wood placed firmly in the ground to 
serve as an anchor for the guys of derricks, etc. 

Deck-bridge : One in which the roadway is carried directly 
at the top-chord joints or on the upper chords themselves. 

Deflection is the bending caused by a transverse stress. 

Ductility is the property of being permanently elongated or 
drawn out. 

Derrick. — A form of hoisting-machine. The peculiar feature 
of a derrick, which distinguishes it from some other forms of 
hoisting-machines, is that it has a boom stayed from a central 
post, which may be anchored but is usually stayed by guys. 

A derrick has one leg, a shears or "A " derrick two, and a gin 
three. A crane has a post and jib. A whin or whim has a vei il- 
eal axis on which a rope winds. Tlu; capstan has a vertical diinu 



DEFINITIONS OF TERMS USED. 503 

for the rope, and is rotated by bars. The windlass and winch 
liave a horizontal barrel. See also Gin-pole. 

Dike, Dyke : A levee or wall of earth to prevent the encroach- 
ment of water or to serve as a wharf or jetty. The constiuction 
varies considerably, according to purpose, exposure, and the 
nature of the foundation. 

Dock. — An artificial excavation or structure for containing a 
vessel for repairs, etc. 

Docks are of various kinds. 

Dry -dock: A dock from which the water is withdrawn after 
the vessel is floated in for repairs. 

Wet-dock: Where vessels are placed to be loaded or unloaded. 

Dog-iron : A short bar of iron, forming a kind of cramp, with 
its ends bent down at right angles and poiuied, so as to hold 
together two pieces into which they are driven ; often used for 
temporary purposes. 

Dredging is the operation of excavating mud, silt, etc., from 
the bottom of rivers, harbors, etc. Machines of various form, 
according to the nature of the service, are employed, as the 
dipper- ^YQ^ge, clam-shell or grapple dredge, crane-dredge, suction 
or hydraulic dredge, ladder- or elevator dredge, etc. 

Drift-pin : A round piece of steel, made slightly tapering, 
and used for drawing holes in two pieces fair or for enlarging the 
holes by being driven through them. 

Dump : An embankment where material is deposited from 
carts, cars, or barrows. 

Dump -scow : A boat having a movable bottom or other con- 
trivance for automatically discharging the load. 

Dutchman : The name given to a block or wedge of like 
material with the structure driven into a gap to hide the fault in 
a badly made joint. 

Eaves : That portion of a roof which projects beyond the 
walls. 

Escarpment : A nearly vertical natural face of rock or soil. 

Eye : A circular hole in a flat bar, etc., for receiving a pin, or 
for other purposes. 

Elasticity ; The property which all materials have (in greater 
or less degree of perfection) of returning to their original figure 
after being disturbed (i. e., strained) by any kind of stress. 

Elastic Limit of materials is defined as that point at whicli 
the deformation ceases to be pr()i)ortional to the stress, or the 
point at which the rate of stretch (or other deformation) begins 



504 DEFINITIONS OF TERMS USED. 

to increase. It is also defined as the poiut at which the first pef- 
Dianeut set becomes visible. 

Fall : The rope used with pulleys in hoisting. 

Factor of Safety. — The ratio in which the breaking load 

exceeds the working load. The factors of safety recommended 

are : 

Dead Live 

Load. Load. 

For perfect materials and workmanship 2 4 

For good ordinary materials and workmanship: 

Metals 3 6 

Timber 4 to 5 8 to 10 

Masonry 4 8 

Fall and Tackle : The fall is the pulling end of the rope ; 
the tackle is the blocks with the rope rove through them. 

False Works : Construction works to enable the erection of 
the main works. Among false works may be cited coffer-dams, 
bridge- centring, scaffolding, etc. 

Fascine : A cylindrical bundle or fagot of brushwood used in 
revetments of earthworks, in making river- and sea-walls, etc. 
They vary in size from 6 to 18 feet in length and 6 to 9 inches in 
diameter. 

Feather-edged : Said of boards when one edge is thinner 
than the other. 

Fender • A piece for protecting one thing from being broken 
or injured by blows from another. 

Fender-piles : Piles driven to ward off floating bodies. 

Fishing : Applied to a form of joint ; uniting by clamping 
between two short pieces which cover tbe joint. 

Flange : A projection from one end or from the body of a 
column, pipe, beam, etc., for the purpose of securing it to another 
piece or to a support. 

Flash-boards : Movable boards placed on the top of a dam or 
weir to retain the water of the stream when the flow is small. 

Fire-proof Construction. — *'The term 'fire proof construc- 
tion ' applies to buildings in which all parts that carry weights, 
stairs, elevator-enclosures and their contents are made of incom- 
bustible material, and in which all metallic structural members 
are protected against the effects of fire by coverings of an iucon- 
bustible and slow-heat-conducting material. As such will be 
considered brick, hollow tiles or buint clay, porous terra-cott;i, 
and two layers of plastering on metal lath. 



DEFINITIONS OF TERMS USED. 505 

" The term * slow-burning construction ' comprises all buildings 
in which the structural members are made wholly or in part of 
combustible material, but throughout which all materials shall 
be protected against injury from fire by coverings of incom- 
bustible, slow- heat-conducting materials." (Chicago Building 
Ordinances, 1893.) 

Flashings : Broad strips of sheet lead, copper, tin, etc., with 
one edge inserted into the joints of masonry an inch or two above 
the roof and projecting out several inches so as to be flattened 
down close to the roof to prevent rain from leaking through the 
joint between the roof and chimney, etc., which projects above it. 

Flush: 1. A term signifying an unbroken or even surface. 
2. To wash by turning on a sudden dash of water, as in cleansing 
sewers by means of flush-tanks. 

Flume : A ditch, trough, or other channel of moderate size for 
conducting water. 

Foundation : The bed or basis of a structure. 

Foxtail : A thin wedge inserted into a slit at the lower end of 
a pin or bolt so that as the pin is driven down the wedge enters 
it and causes it to swell and hold more firmly. 

Frame : The skeleton of a structure; to put together pieces so 
lis to form a frame. 

FuRRiNGS : Pieces which are placed upon others which are too 
^ow merely to bring their upper surfaces up to a required level, as 
is often done with joists when one or more are too low^; a kind 
of chock. 

Fusibility is the property of becoming fluid when subjected to 
heat. The temperature at which this is effected differs in each 
metal, and is called the melting -point. 

Gasket : Rope-yarn or hemp used for stuflSng at the joints of 
water-pipes, etc. 

Gin-pole : A timber mast with four guys and a sheave at the 
top over which the hoist-line leads to a crab bolted three or four 
feet from the bottom. 

Girder. — The name girder is generally applied to beams of iron 
and steel, whatever the form, either cast, solid, lolled, or built up 
of plates and angles or other shapes riveted together. A *' riveted 
girder" means a girder made of plates and angles; a "girder- 
beam" means a girder made of a solid rolled beam; a" box- 
girder" is composed of two girders joined together by cover- 
plates, etc.; a ''double girder" signifies the use of two rolled 
beams in a girder, 



506 DEFIJN^ITIONS OF TERMS USED. 

Grubbing : Removing roots aud stumps from the surface. 

Gussets . Plain triangular pieces of plate iron riveted by their 
vertical and horizontal legs to the sides, tops, and bottoms of box- 
girders, etc., for strengthening their angles. 

Guy : A stay -rope passing from the top of a spar or mast to a 
post or anchor in the ground, as the guys of a derrick, etc. 

Hardening : The property of becoming very hard when heated 
aud quenched. 

Hardness is the property of resisting indentation or wear by 
friction. 

Handspike : A loose bar forming a lever for lifting or shifting 
an object. 

Hardpan : Gravel cemented vrith clay, v^hich it is sometimes 
necessary to blast. 

Hip-roof : One that slopes four v^ays, forming ridges or hips. 

Hoarding : A temporary close fence of boards placed around 
a work in progress to exclude stragglers. 

Horse : A wooden bar with legs used for supporting a staging. 

Impost : The upper part of a pier from which an arch springs. 

Jam-nut : An auxiliary nut screwed down upon another one 
to hold it in plac '; cleck-nut, lock-nut. 

Jack ; A raising instrument, consisting of an iron rack in con- 
nection with a short, stout timber which supports it, and worked 
by cog-wheels and a winch. 

Jack screw : A lifting implement which acts by the rotation 
of a screw in a threaded socket. 

Jetty: A construction of stone, wood, etc., projecting into 
the sea, and serving as a wharf or 'pier for shipping, or as a moU 
to protect a harbor. 

Jib : The upper projecting arm of a crane, supported by the 
stay. 

Jim CROW : An implement for bending or straightening rails. 

Kerf : The opening or narrow slit made in sawing. 

Knee : A piece of metal or wood bent at an angle to serve as 
a bracket. 

Lap : To place one piece upon another, with the edge of one 
reaching beyond that of the other. 

Lap-welding : Welding together pieces that have first been 
lapped, in distinction to huttioelding. 

Lead : The length of haul from the pit to the dump. 

Light: A pane of window-glass. 

Lining : The masonry walls and arch built in a tunnd* 



DEFINITIONS OE TERMS USED. 507 

Lintel : A Jioiizoutal beam over an opening in a wall. 

Live Load : A load which is applied suddenly. 

Load : The weight upon a beam or structure ; it may be either 
concentrated at the centre or other point or uniformly distributed. 

Lock (Canal). — A canal-lock is a device by which boats are 
passed from one level to another. It consists of a basin between 
the levels, having a pair of gates at each end communicating 
with the respective level. The floor of the upper end is even 
with the upper level, and the lower floor with the lower level. 

The parts of a lock are : 

The head-gate and the tail-gaie, which, with the side walls, 
enclose the lock-chamber. The gates are made of framing, with 
leaf-planking nailed and bolted thereto. 

The clap-sill or mitre-sill, with two branches, is the framing 
against which the lower edge of the gate shuts. 

The hollow quoin is the recess in the masonry occupied by the 
heel-post of the gate. 

The head-bay is the canal above the lock. 

The tail hay is the canal below the lock. 

The lift is the amount of fall overcome by the lock. 

The lift-wall is the wall at the foot of the head-gate. 

Louvre : A kind of vertical window placed on the roofs cf 
workshops, etc., and formed of slats which permit ventilation 
and exclude rain. 

Lumber: Sawed timber, either boards, plank, or squared 
pieces. 

Malleability is the property of being permanently extensible 
in all directions by hammering or rolling. 

Maul : A large mallet of hardwood. 

Mill Construction. — The term **mill construction " applies 
to buildings in which all the girders and joists supporting floors 
and roof have a sectional area of not less than 72 square inches, 
and above the joists of which there is laid a solid timber floor not 
less than 3f inches thick. Wooden posts in buildings of this class 
are to have an area of at least 100 square inclies. Iron columns, 
girders, or beams must be protected by an incombustible slow- 
heat-conducting material, but the wooden posts, girders, and joists 
need not be covered. (Chicago Building Ordinances, 1898.) 

Modulus or Coefficient of Elasticity is a number express- 
ing the relation between the amount of extension or compression 
of a material and the load producing that extension or compres- 
sion ; it is obtained by dividing the stress in pounds per square 



508 DEFIIl^ITIONS OF TERMS USED. 

inch of sectional area by the elongation or contraction expressed 
as a fraction of the length of the specimen. 

Muck : Soft mud containing much vegetable matter. 

Mucking : Removing muck. 

Neat Lines : Tiiose by which tlie work is laid out. 

Neat "Work : Work wrought to the neat lines. 

Nosing : The slight projeciion upon the front edge of a step 
or window-sill. 

Out of Square : Askew, oblique. 

Out op Wind : Perfectly straight or flat. 

Pliability : The ability of a body to change its form tempo- 
rarily under different stresses. 

Proof Load : The greatest load that can be applied to a piece 
of material to prove or test it by straining it to the utmost ex- 
tent without producing permanent deformation or injury. 

Parget : The plastering applied to the interior surface of 
chimneys. 

Plant : The tools and apparatus required in any operation. 

Pig : An oblong mass of iron as run from the smelting-fur- 
Dace. 

Pile : Spars pointed at one end and driven into the ground 
(see Piles, page 215 et seq.). Spile is a corruption. 

Pilot-nut : A nut placed on a truss-pin to protect the thread 
and assist in guiding the pin while it is being driven. 

Pony-truss : A low truss, of short span, without overhead 
lateral bracing, and with the roadway carried at the bottom 
joints. 

Primed : Having the first coat of paint or "priming " laid on. 

Profile : A light wooden frame set up to guide workmen 
during construction ; a longitudinal section through a roadway, 
etc. 

Quicksand may be defined as a mass of sand, or of silt and 
argillaceous matter, intimately mixed with water, forming a 
semi-fluid, having all the properties of a fluid, but in a minor 
degree. 

Ramp : An inclined platform used instead of steps. A con- 
cave sweep connecting a higher and lower portion of a railing, 
wall, etc. 

Racked Back : Built in steps or offsets. 

Raked Out: Cleaned out \\\i\\ a scraper. 

Return : The termination of the drip-stone or hopd-moulding 
of a door or window. 



DEFINITIONS OF TERMS USED. 509 

Reveal : The sides of an opening for a doorway, window, 
etc., between the framework and the outer surface of the wall. 

Resilience is a term used to express the quantity of "work 
done " in deforming a piece of material up to the elastic limit by 
the application of auy kind of stress. 

Saddle HEADS : Hollow, castings resting on the heads of 
columns to sustain another series above and allow beams to pass 
through. 

Scaffold : A platform temporarily erected during the prog- 
ress of a structure for the support of workmen and materials. 

Scow ; A flat-bottomed, square-ended boat, employed for many 
purposes— carrying materials, supporting pile-drivers, etc. 

Scribe : To trim off the edge of a board, etc., so as to make it 
fit closely at all points to an irregular surface. 

Separators : Thimbles or small pieces of iron inserted be- 
tween girders to keep them apart. 

Set {n.): A permanent bend or deflection produced by strain- 
ing a beam beyond its limit of elasticity. 

Set {v.) : Hardened, as the hardening of cement. 

Sewage : The matter borne off by a sewer. 

Sewerage : The system of sewers. 

Shackle or Clevis : A link in a chain shaped like a U, and 
so arranged that by drawing out a bolt or pin which fits into 
two holes at the ends of the U the chain can be separated at that 
point. A U-shaped metallic strap used in connection with a 
pin to connect a draft-chain or tree to a plough, etc. 

Shim : A piece of wood, stone, or iron let into a slack place 
to fill it out to a fair surface or line. 

Shaft : A vertical pit or well. 

Shoes : Iron fittings at the ends of rafters, etc. 

Shoot : An inclined trough through which materials are slid. 

Shore : A prop. 

Shearing Stress : The stress produced when one part of a 
body is forcibly pressed or pulled so as to tend to make it slide 
over another part. 

Silt : Soft, fine mud. 

Sinking : Digging a vertical shaft. 

Siphon or Dive-culvert : A culvert built in the shape of a 
U for carrying a stream under an obstacle and allowing it after- 
wards to rise again to its natural level. 

Skid : Slanting timbers forming an inclined plane, used in load- 
ing or unloading heavy articles from a truck, wagon, etc. 



510 DEFINITIONS OF TERMS USED. 

SKb:LETON Construction : A framework of metal which 
transmits all the external aud internal strains from the top of a 
building to the foundation. 

Slings: Pieces of rope or chain put around stones, etc., for 
raising them by. 

Slip : The sliding down of the sides of earth cuts or embank- 
ments. A long, narrow water-space or dock between two 
wliarves or piers. 

Sluice : A water-channel of masonry, wood, etc., furnished 
with gates to regulate the flow of the water. 

Sodding. — The placing of grass sods on the slopes of embank- 
ments or other surfaces. 

The sods are cut from their bed in long strips with a sharp 
spade or on a large scale with a paring-plough. The strips are 
rolled with the grass inward for transportation to the place of 
use. On slopes they are held in place by small pegs driven at 
suitable intervals, and are tamped or beaten down to a solid bear- 
ing with a square or oblong mallet, called a flattening-mallet. 
Ragged and torn edges are removed or pared with a curved 
knife. 

Spandrel-beam : See Beam. 

Splay : A surface making with another an angle differing 
from a right angle. 

Spile. — The name spile is frequently but incorrectly given to 
piles. 

A spile is a small plug of wood used for stopping the spile-hole 
of a barrel or cask. The spile-hole is a small aperture made in 
the cask when placed on tap, usually near the bung-hole, to afford 
ingress for the air in order to permit the contained liquid to flow 
free\y. 

Splice : To unite two pieces firmly together. 

Stage : The interval or distance between two platforms in 
shovelling, throwing, or lifting. 

Stiffness or Rigidity : The resistance offered by bodies to 
change of their form under stresses. 

Stone boat: A flat-bottomed sled for haulingheavy stones for 
short distances. 

Strength : The resistance offered by materials to deforma- 
tion. 

Stresses : Stress and strain are words often used indifferently, 
either to mean the alterations of figure produced in a body by 
any forces, or to mean the forces produciuir those alterations. 



DEFINITIONS OF TERMS USED. 511 

Materials are subject to the undermentioned stresses, which 
produce strains, and, when carried far enough, fracture as 
stated. 

Stress. Strain. Mode of Fracture. 

Tensile or pulling | K^S [ Tearing 

Compressive or thrust- j Shortening } n.^,^^\,i^^ 
ing (Squeezing f ^lushmg 

Transverse or bending Bending Breaking across 

Shearing Distortion Cutting asunder 

Torsional or twisting Twisting j'^lSr"' "^'"""^'"^ 

Stirrup : A pendant band of iron supporting girders. 

Stringers : Longitudinal beams, generally used to support 
uniform loads. 

Strut : An oblique brace ; the member of a truss which is 
compressed endwise. 

Stud : A short, projecting pin. 

Stud BOLT : A bolt with a screw cut upon each end, one end 
to be screwed permanently into something, and the other end to 
hold by a nut something else that may be required to be removed 
at times. 

Sump : A well dug at the lowest point of the work into which 
the rain and other water may be led and from which it is re- 
moved by pumps. 

SwEDGED : Hammered with a swedge-hammer. 

Swivel : A revolving link in a chain, consisting of a ring or 
hook ending in a headed pin which turns in a link. 

Tamp : To compact loose earth by ramming ; to fill up with 
sand, etc., the remainder of the hole in which an explosive has 
been placed for blasting. 

Tap-bolt : A bolt which simply passes into its socket without 
penetrating it. 

Templet : A form or pattern to guide workmen. 

Tempering : Lowering the degree of hardness after harden- 
ing, by reheating and cooling at different temperatures. 

Tension is the stress produced by pulling. It elongates the 
material upon which it acts, and tends to cause rupture by tear- 
ing it asunder. 

Thickening- washers : Additional washers used when the 
thread is not cut far enough on a bolt. 



512 DEFINITIONS OF TERMS USED. 

Thimble : A short piece of tube slipped over a rod to separate 
parts of a structure, as a post or chord. 

Through Bridge : One in which the roadway is carried direct- 
ly at the bottom- chord joints, with lateral bracing overhead be- 
tween the top-chord joints, thus enclosing a space through which 
the load passes. 

Torsion : A twisting strain, which seldom occurs in building, 
construction, though quite frequently in machinery. 

Transverse Stress is one caused by bending the material on 
which it acts, and it tends to break it across. 

Truss. — A framed or jointed structure designed to act as 
a beam. It is composed of two longitudinal members called 
the upper and lower chords. The members which join the chords 
are called the wehmemhers; these comprise struts, ties, and counter- 
braces. The struts are sometimes called jposU or columns. The 
spaces between the chord-joints are called panels. 

TuRNBUCKLE : A Small fastening turning about a screw 
through its centre ; a nut with a right- and left-hand screw for 
tightening up rods. 

Waste-weir — Spillway: An overfall provided along a 
canal, reservoir, etc., at which the water may discharge itself in 
case of becoming too high by rain, etc. 

Wasted : Thrown away. 

Web : The flat metallic surface connecting two or more ribs 
or flanges. 

AYeir : An opening in the breast of a dam or an embankment 
to discharge the excess of water; also an opening used for 
measuring the quantity of water discharged. 

Weld : The junction of two metals made by heating and ham- 
mering them together in connection with a flux. 

Wind : Synonj^mous with twist, warp, etc. 

Wing-walls : The retaining walls which flare out from the 
ends of bridges, etc. 

Underpinning : Supports, temporary or permanent, intro- 
duced beneath a wall already constructed. 

Upset : Hammered back to thicken the end of an iron bar, as 
in forming an eye or head for a bolt. 

Valley : A re-entrant angle formed by the intersection of two 
parts of a roof. 

Wales : Longitudinal timbers placed on the sides of piles. 

Warped : Twisted ; out of line. 



DEFINITIONS OF TERMS USED. 513 

Washers : Broad pieces of metal surrounding a bolt, and 
placed between the faces of the timbers through which the bolt 
passes and the head and nut of the bolt so as to distribute the 
pressure over a larger surface, and prevent the timber from being 
crushed when the bolt is tightly screwed up. 

Yield-point is defined as that point at which the rate of 
stretch (or other deformation) begins to increase rapidly. The 
difference between the elastic limit, defined as the point at which 
the rate of stretch begins to increase, and the yield-point, al 
which the rate of stretch increases suddenly, may in some cases 
be considerable, ^ 



514 LIST OF AUTHORITIES COISTSULTED. 

LIST OF AUTHORITIES CONSULTED. 

Any of the following works may be profitably studied by those 
desiring further information upon the subjects treated of : 

Allsop, F. C: Practical Electric-light Fitting. 

Baker, I. 0.: Masonry Construction. 

Brande : Encyclopaedia of Science, Literature, and Art. 

Barba, E. S.: The Use of Steel for Constructive Purposes. 

Berg, Be C: Safe Buildings. 

Birkmire, W, H.: Architectural Iron and Steel. 

Bolland, 8.: The Iron-founder. 

Buchan, W. P.: Plumbing. 

Bell 's Carpentry. 

Byrne, A. T.: Highway Construction. 

Clark, 1\ M.: Building Superintendence. 

Carnegie's Pocket Companion. 

Campin, F. : Construction of Iron Roofs. 

Church, A, H.: Chemistry of Paints and Painting. 

Cameron, K.: Plasterer's Manual. 

Davis, C T. : Bricks, Tiles, and Terra-cotta. 

Drinker, E, S.: Tunnelling, Explosive Compounds, and Rock- 
drills. 

Engineering and Building Record. 

Engineering Magazine. 

Engineering News and American Railway Journal. 

Fanning, J, T.: Treatise on Hydraulic and Water-supply En- 
gineering. 

Foster, W. C. : Wooden Trestle-bridges. 

Foster, J. G.: Submarine Blasting. 

Gould, L. : Carpenter's and Builder's Assistant. 

Gilmore, Gen, Q, A.: Limes, Hydraulic Cements, and Mortars; 
Construction of Roads, Streets, and Pavements. 

Gillespie, W, M.: Principles and Practice of Road-making. 

GiUtmann, 0.: Blasting. 

Heath, A. H.: Manual on Lime, and Cement. 

Hammond, A, : Brick and Tile Book. 

Hodgson, F. T.: Practical Carpentry. 

Haswell, C. H: Mechanics' and Engineers' Pocket-book. 

Haupt, L, M.: Engineering Specifications and Contracts. 

Hoskins, G. G.: Clerk of Works. 

Hurst, J. T.: Architectural Surveyors' Handbook. 

Hicks, I. P.: Builders' Guide. 



LIST OF AUTHORITIES CONSULTED. 5ii; 

Johnson, J. B.: Eugineering Contracts and Specifications. 

Johnson, Bryan, and Turneaure : Theory and Practice of 
Modern Framed Structures. 

Jones, /?. H.: Asbestos. 

Joynson, F, H.: The Metals used in Construction. 
[ Kent, W.: Mechanical Engineers' Pocket-book. 

Kidder, F. E.: Building Construction and Superintendence; 
The Architects' and Builders' Pocket-book. 

Kirk, E.: The Founding of Metals. 

Knight, E. II.: Mechanical Dictionary. 

Kirk, A.: The Quarryman and Contractor's Guide. 

Latham, B,: Sanitary Engineering. 

Love, E. G,: Pavements and Roads: Their Construction and 
Maintenance. 

Mahan- Wood : Civil Engineering. 

Moncton, J.: Stair-building. 

Macfarlane, J. W. : Notes on Pipe-founding. 

Merrill, G. P.: Stones for Building and Decoration. 

Metcalf, Wm.: Steel. 

Notes on Building Construction. 

Newman, J.: Scamping Tricks ; Notes on Concrete and Works 
in Concrete, 

Nystrom, J. W.: Pocket-book of Mechanics. 

Patton, W. M. : Civil Engineering ; A Practical Treatise on 
Foundations. 

Powell, G. T,: Foundations and Foundation Walls. 

Pencoyd Iron Works: Wrought Iron and Steel. 

Rankine, W. J if..* Civil Engineering. 

Beid, H. : Natural and Artificial Concrete. 

Smeaton, J.: Plumbing Drainage. 

Smith, J. B.: Wire Manufacture and Use. 

Spalding, F, P.: Testing and Use of Hydraulic Cement. 

Seddon, H. C: Builders' Work and the Building Trades. 

Spon's Dictionary of Engineering. 

Staley and Pierson : Separate System of Sewerage. 
Trautwine, J. C: Civil Engineers' Pocket-book. 

Thurston, R. H.: Materials of Engineering. 
Vodges, F. W.: The Architect and Builder's Pocket Companion. 
Walsh, M.: Brick-making. 

Webb, T, W.: Guide to the Testing of Insulated Wires and 
Cables. 

Warren, W. II.: Engineering Construction in Iron, Steel, and 
Timber. 



INDEX. 



Absorptive power of bricks, 24 
stones, 6 
wood, 75 
Abutment, 259-275 
Abutting joint, 281 

Acid and basic processes of steel- 
making, 110 
Acid tests for iron and steel, 124 
Activity of cement, 39 
Adulteration of cement, 35 

linseed oil, 344 
red lead, 342 
white lead, 341 
Air-slaked lime, 31, 32 
Alkalies in brick-clay, 18 
Alloys, 142 

of steel, 114 
Altars, 499 
Aluminum bronze, 142 

shrinkage of, 148 
Angle bead, 293 
rafter, 286 
staff, 293 
tie, 293 
Annealing steel, 129 
Apron, 499 
Aqueduct, 499 
Arch- brick, 20 
Arches, brick floor, 301 
Arched beam, 294 
Arches, centring for, 277 
concrete floor, 305 
construction of, 276 
definition of the parts of, 275 
description of, 274 
flat tile, 303 
Arch sheeting, 275 

stones, cutting of, 232 
Arches, striking centres, 277 
Architrave, 290 
Area covered by a cubic yard of 

broken stone, 384 
Area covered by a cubic foot of ce- 
ment, 335 
Argillaceous stones, 5, 11 
Arris, 259-499 

glitter, 286 
Artificial foundations, 211a 

stone pavements, 387 



Artificial stones, composition of, 29 

Asbestos, 156 

felt, 158 
paper, 158 
Ash, inspection of, 87 

white, 56 f 

green, 56 
red, 56 
Ashlar masonry, 248 \ 

Ashlaring, 293 -X 

Asphalt, 43, 48 

Alcatraz, 50 

felt, 158 

mastic, 380 

paving compositions, prepa* 

ration and laying, 381 
Pittsburg flux, 51 
Utah liquid, 50 
Asphalte, 46, 47 
Asphaltene, 45 
Asphaltic cement, 49 

manufacture of, 49 
concrete, 229 
paving materials, 374 
Asphaltum, 43 

analysis of, 52 
asphaltene, 45 
Berraudez, 378 
California, 379 
characteristics of, 43 
coating for pipes, 356-364 
composition of, 47 
crude, 48 
description of, 43 
distribution of, 46 
earthy, 43 
elastic, 44 
flux for, 49 
gilsonite, 46 
hard, 44 
lithocarbon, 47 
maltha, 46 
nomenclature of, 47 
occurrence of, 46, 
oiling of, 49 
origin of, 45 
petrolene, 44 
refined, 48 
refining of, 48 
residuum oil for, 51 
retine, 45 

617 



518 



IN^DEX. 



Asphaltum, solvftnts for, 44 

specific g:ravity of, 44 

tests for, 52 

Trinidad, 376 

uintahite, 46 

varieties of, 43 

wurtzilite, 46 
Astragal, 293 
Atmosphere, effect of, on stone, 7 

test for effect on stone, 7 
Axed stone, 237 
Axles, tests for, 145 



Backing, 259 

Baluster, 288 

Balustrade, 288 

Ballast, 499 

Barff's process of coating pipes, 356 

Barge board, 286 

Barge couple, 293 

Basalt, 9 

Base, 290, 499 

Basic steel, 110 

Basil, 499 

Batter, 293 

Battlement, 499 

Bay, 283 

Bead, 293 

and butt panel, 290 
and quirk panel, 290 
butt and square, 290 
flush panel, 290 
Beams, 293, 499 

anchorage of, 283, 300 
bearing of, on walls, 283, 299 
connecting, 299 
setting parallel, 299 
Beard, 294 
Bearer, 294 
Bearing, 499 

blocks, 259 
pla:e, 499 
piles, 215 

power of soils, 211 
stress, 499 
Bed, natural, of stone 5 

plates, 499 
Beetle, 499 
Belt course, 259 
Belted timber, 74 
Berme, 499 

Bermudez asphaltum, 378 
Bessemer pig iron, 91 

steel, 110 
Bethell's process for preserving tim- 
ber, 67 
Bevel, 499 
Bevelling, 294 
Binders, 259 
Binding joist, 283 
Bird's mouth, 294 
Bitumen, 43, 48 

origin of, 45 
Bituminous limestone, 48 

rock, test for, 53 
sandstone, 48 



Black walnut, inspection of, 87 
Blasting, precautious to be observed, 

206 
Blasting rock, 204 
BHnd bond, 260 
Blister-steel, 109 
Block, 294, 500 

and tackle, 500 
Blocking, 500 

course, 259, 262 
Block-and-cross bond, 260 
Block-tin pipe, 320 
Blue sap, 76 
Board, 294 

measure, 72 
Boards, fencing, grade of, 81 
roofing, 79 

rules foi- grading common, 81 
Boiler-iron, tests for, 145 
Bolster, 294, 500 
Bolts, and nuts, 183 

dummy, 184 

strength of, 187 

tests for, 145 

varieties of, 183 
Bond in masonry, 249, 259 

stones in piers, 260 
Bonding course, 262 
Boning, 500 
Bore, 500 
Borrow-pit, 500 
Boulder, 500 
Box frame, 294 
Brace, 294 
Brash in timber, 74 
Brass, 142 

shrinkage of, 148 

weight of sheet (Table 16), 133 

wire, weight of (Table 16), 133 
Break joint, 500 
Breaking-load, 500 
Breakwater, 500 
Breast-summer, 294 

wall, 500 
Brick, absorptive power of, 24 

arch, 20 

arches for floors, 301 

arches, tie-rods for, 302 

ashlar, 260 

body, 20 

character of clay for, 18 

characteristics of good build- 
ing, 24 

characteristics of good paving, 
385 

cherry, 20 

classification of, 19 

clinker, 20 

color of, 19 

compass, 21 

crushing strength of (Table 4), 
23 

definition of, 18 

effect of frost on, 25 

enamelled, 22 

feather-edge, 21 

face, 21 

front, 21 

glazed, 22 



INDEX. 



519 



Brick, hard, 20 

hard kiln-run, 21 
hollow, weight of, 23 
inspection of, 24 
kiln-run, 21 
laying paving, 886 
machine-made, 20 
manufacture of, 18 
pale, 20 
pavement, 385 
pressed, 20 

properties of paving, 387 
rank of, 21 
re-pressed, 20 
Roman, 23 
salmon, 20 
sanded, 20 
sewer, 21 

size of building, 23 
size of paving, 387 
slop, 20 
soft, 20 
soft mud, 20 

specific gravity of (Table 4), 
23 

stiff mud, 20 
tests for building, 24, 145 
tests for paving, 385 
transverse strength of, 24 
weight of, 23 
weight per cubic foot (Table 4), 

23 
weight of paving, 387 
masonry, amount of mortar 

required for, 256 
masonry, bond of, 260 
masonry, cleaning down front, 

257 
masonry, effloresence on, 258 
masonry facework, 256 
masonry, general rules to be 

observed in laying, 254 
masonry impervious to water, 

257 
masoiiy, laying the bricks, 254 
m^asonry, running bond, 256 
masonry, Sylvester's washes 

for, 257 
masonry, thickness of joints in, 

256 
masonry, wetting the brick, 

255 
masonry, white jointwork, 257 
Bridge board, 295 
truss, 500 
Bridging floors, 283 
Bright sap, 77 
Brittleness. 500 
Broken ashlar masonry, 250 

stone, area covered by a cubic 
yard, 384 
pavements, 383 
voids in, 384 
weight of, 384 
Bronze, 142 

Brownstone. See Sandstone. 
Build. 260 
Built beam, 294 
Bulkhead, 500 



Burnet's process for preserving tim- 
ber, 66 
Bush-hammered stone, 237 
Butt, 500 
Butt-joint, 281 
Buttress, 260 



Calcareous stones, 5-11 

Calibre, 500 

California asphaltum, 379 

Calipers, 500 

Calk, 501 

Calking joints of cast-iron pipe, 357 

of rivets, 193, 196 
Camber, 275, 501 
Cant-hook, 501 
Cantilever, 501 
Carbon in steel, 112 
Carpentry, architraves, 290 
base board, 290 
beams, anchorage of floor, 

283 
beams, bearing of floor, 

283 
bevelling ends of floor- 
beams, 283 
bridging floors, 283 
doors, 289 

parts of, 289 
floor-beams, 283 
flooring, 282 
inspection of, 279 
joints in, 280 
joining beams, 280 
linings, 291 
mouldings, 291 
parts of floors, 283 
roof-framing, 286 
rules governing trimming, 

284 
stairs, 287 

parts of, 288 
standing finish, 290 
terms used in, 293 
trimmer-beams, 284 
trimming floor-beams, 284 
wainscoting, 291 
wall-plates, 287 
windows, 292 
Cast-iron, appearance of, 98 

castings, defects of, 97 
columns, inspection hole, 98 
compression of, 95 
contraction of, 95 
description of, 94 
effect of manganese on, 92 
phosphorus on, 92 
silicon on, 93 
sulphur on, 92 
elongation of, 95 
examining water-pipes, 98 
expansion of, 95 
extension of, 95 
inspection of, 98 
melting-point, 95 



520 



INDEX. 



Cast iron, notes on founding, 97 
piles, 216 

pipe, defects of, 354 
pipe, inspection of, 354 
pipes, coating for. 355 
pipes, dimensions and 

weights of, 360 
pipes. Dr. Smith's coating 

for, 355 
pipes, hydraulic test for, 356 
pipes, test for quality of 

metal, 355 
properties of, 95 
remelting. 94 
shrinkage of, 96, 148 
size of test-pieces, 98 
soil-pipe, 320 
strength of, 96 
tenacity at high tempera- 
tures, 96 
test-bars, 98 
test for honeycomb, 98 
tests for, 145 
varieties of, 94 
weight of, 95 

weight of plates, round and 
square bars (Table 10), 99 
Cast steel, 111 

tests for, 121 
Castings, steel, 121 
Causeway, 501 
Cedar, white, 56 

red, 56 
Ceiling lumber, dimensions of yellow 
pine, 83 
grade of, 80 
Cement, activity of, 39 

adulteration of Portland, 35 
amount of mortar made from 

a barrel, 38 
asphaltic, 49 

manufacture of, 
49 
ball test for, 37 
blowing and swelling of 

Portland, 35 
characteristics of Portland, 

34 
clay in Portland, 34 
color of Portland, 34 

Rosendale, 35 
cubic feet in a barrel, 38 
bushel, 39 
dimensions of a barrel. 38 
excess of lime in Portland, 34 
expansion and contraction of 

Portland, 34 
fineness of, 39 

Portland, 34 
Rosendale, 35 
form of label for sample, 36 
gypsum in Portlan(i, 41 
hydraulic activity, 40 

eneigy of, 40 
hydraulicity of, 40 
increase in bulk, 38, 243 
; inspection of, 36 
Keene's, 326 
Lafarge, 43 



Cement, length of sewer-pipe One bar- 
rel will lay, 370 
manufacture of Portland, 34 

slag, 42 
market forms, 38 
marking rejected packages 

of, 36 
measuring of, for mortar, 243 
miscellaneous, 42 
mortar, effect of frost on, 40 
mixing of, 243 
salt in, 40 
natural, 35 

overlimed Portland, 35 
pipe test for, 367 
Portland, composition of, 34 

quality of, 34 
preservation of, 38 
pozzuolana. 43 
quick and slow setting, 40 
Roman, 43 
Rosendale, 35 

setting of, 35 
underburned, 35 
sampling of, 36 
setting of, 41 

Portland, 34 
size of sieves for measuring 

fineness of, 39 
slag, 42 

soundness of, 41 
specific gravity of Portland, 

34 
storing of, 38 
strength of, 41 
sulphate of lime in water 

used in mixing, 40 
temperature of water used 

in mixing, 41 
tensile strength of Portland, 

34 
test for contraction, 37 
expansion, 37 
setting, 37 
slag, 43 
soundness, 37 
tests for, 37, 145 
underburnt Portland, 34 
variation in bulk of, 38 
weight of a barrel. 38 
bushel, 39 
cubic foot. 39 
PorUand, 34 
Rosendale, 35 
Cementing materials, 30 
Centring for arches, 277 
Chain-bond, 259 
Chairs, 501 
Chamfer, 295, 501 
Chamfered panel, 290 
(^hecks in timber, 74 
Chemical classification of stones, 5 
numeration of steel, 115 
Cherry, inspection of, 87 
Cherty limestone, 11 
Chilling irons, 94 

Chipping-chisel, 501 > 

piece, 501 i 

Chock, 501 .• :- «v"4^ 



INDEX. 



521 



Chrome steel, 115 
Circle, properties of, 410 
Circles, area and circumference, 411 
Clapboard, 294 
Classification of brick, 19 
of stones, 4 
Clay, character of, for brick, 18 
composition of, 153 
definition of, 153 
in Portland cement, 34 
iron in brick, 18 
puddle, 223 

puddling, 223 
quality of clay, 222 
test for quality of, 223 
refractory, 153 
slate, 11 
Cleaning down masonry, 260 
Clearing, 501 
Cleac, 295 

Cleavage-line of rocks, 4 
Clevis, 501 
Close piles, 215 
Closers, 260 
Coal-tar, 156 

coating for pipes, 356 

steel pipes, 364 
distillate, 373 
Coating cast-iron pipes, 355 
Coffer-dams, 212 
Collar-beam, 286 
Color of bricks, 19 
Column castings, 96 

bearings, 298 
Columns, erection of, 298 
Common boards, rules for grading, 81 

rot in timber, 65 
Composition of pig-iron, 91 

wrought iron (Table 
11), 102 
Compressed steel, 115 
Compression, 501 

of cast iron, 95 
Concrete, appearance of well-mixed, 
226 
asphaltic, 229 
definition of, 224 
depositing under water, 228 
floors, 305 
inspection of, 226 
laitance, 229 
laying of, 227 
mixing of, 226 
necessity of constant in- 
spection, 226 
pipes, 367 

precautions to be observed 
when depositing in layers, 

227 
proportions of materials in, 

225 
qualities essential to good, 

224 
quality of the materials, 

224 
quantity of materials re- 
quired for 1 cubic yard, 
225 
ramming of, 227 



Concrete, strength of, 224 

weight of, 224 
Contraction of cast iron, 95 
metals, 148 
Portland cement, 34 
steel, 112 
wrought iron, 103 
Conventional signs for rivets, 192 
Copper alloys, tests for, 145 

description of, 132 

expansion of, 132 

melting-point of, 132 

nails, 174 

roofing, 314 

shrinkage of, 148 

strength of, 132 

tests for, 132 

weight of, 132 

round (Table 15), 

132 
sheet (Table 16), 133 

wire, weight of (Table 16), 133, 
(Table 27) 165 
Coping, 261 
Corbel, 261, 295, 501 
Cornice, 261 
Corrugated iron. 313 
Counterbrace, 501 
Counterfort, 262 
Countersink, 501 
Course, 262 
Covering-stones, 501 
Crab, 501 

Cracks in timber, 74 
Cradle, 502 
Cramps, 262 
Crandalled stone, 237 
Crane, 502 
Creosote, 157 
Creosoting timber, 67 
Crest, 295. 502 

railing, 502 
Cribs, 212 

Crooks in timber, 76 
Cross-bond, 259 
Cross-strain, 502 
Crowbar, 502 
Crown, 275 
Cube roots, 416 
Cubic measure, 391 
Culls, 87 
Culled, 502 
Culvert, 502 

Cup-shake in timber, 74 
Curb, 502 
Curbstones, 388 
Curtain-wall, 502 
Cut nails, 174 

Out stone, inspection of, 241 
Cut-water, 262, 442 
Cypress, 57 



D 



Dado, 295 
Dam, 502 
Dead load, 502 
Deadman, 502 



[iiiiiLmiiiiniiiiicmmi 



522 



INDEX. 



Decay of timber, 64 

Decirnal equivalents for fractions of 

an inch, -"394 
Deok-hridcre, 502 
Defects of cast-iron castings, 97 
pipes, 354 
granite, 16 
limestone, 16 
sandstone, 16 
steel ingots, 118 
terra-cotta, 26 
timber, 74 
Deflection. 502 
Derrick, 502 

Destruction of timber by worms, 65 
Detection of dry rot, 65 
Diagonals, 295 
Diary, inspector's, 2 
Dike, or dyke. 503 
Disk-piles, 215 

Dismissal of incompetent workmen, 2 
Distribution of asphaltum, 46 
Dive-culvert, 509 
Doatiness in timber, 74 
Dock, 508 
Dog-iron, 503 

Doors, construction of, 289 
hardwood, 289 
pine, 289 
panelled, 289 
Dots, plastering, 325 
Dowels, 262, 295 
Dovetail, 295 
Drafted stones, 231 
Dragon-beam. 286 
Draw-bore, 295 

Dredging, duty of inspector, 207 
extra allowance in, 207 
increase of scow over place 

measurements, 207 
manner of performing, 207, 

503 
marking limits of, 207 
Drift-bolts, 183, 213 

holding power of, 184 
Drift-pin, use of, 126, 503 
Drilling, rate of progress, 203 

rock, 203 
Dry measure, 391 

rot, detection of, 65 

in timber, 64 
stone walls, 262 
Ductility, 502 
Dummy bolts, 184 
Dump, 503 
Dump-scow, 503 
Durability of stone, 5 

timber, 64 
Dutchman. 503 
Duty of inspectors, 1 
Dynamite, 205 



E 

Earth excavation, 201 

removing of. 202 
Earthwork, definition of, 198 

duty of inspector, 198 



Earthwork, form of side-slopes, 200 

increase and shrinkage of 
excavated material, 200 
prosecution of, 198 
slopes of, 199 
Eaves, 286, 503 
Edge-grain timber, 77 
Edge-nailed, 282 
Edge-shot, 294 

Efflorescence on brick masonry, 258 
Elastic limit, 503 
Elasticity, 503 

Electrical conductivity of cast iron, 95 
copper, 182 
lead, 134 
steel, 112 
tin, 136 
wr't iron, 102 
zinc, 141 
Elm, white, 57 
Elongation of cast iron, 95 
measuring, 147 
of wrought iron, 103 
Embankments, manner of forming,208 
Enamelled brick, 22 
Encaustic tiles, 28 
English bond, 260 
Escarpment, 503 

Excavation, amount of material loos- 
ened per man, 201 
classification of, 198 
earth, 201 
rock, 203 
Expansion of cast iron, 95 
copper, 132 
lead, 134 

Portland cement, 34 
steel, 112 
timber by heat, 64 

water, 63 
tin, 136 

wrought iron, 102 
zinc, 141 
Explosives, 204 
Extension of cast iron, 95 
steel, 112 
wrought iron, 103 
Extrados, 275 
Eye, 503 



Face, 262 
Facine, 504 
Facing, 262 
Facia-board, 286 
Factor of safety, 504 
Fall, 504 

and tackle, 504 
False pile, 216 

works, 504 
Fastenings, 174 
Feather-edged. 204, 504 
Felt asbestos, 158 

asphalt, 158 

laying on roofs, 307 

sheathing, 158 

tar, 158 
Fencing, grade of lumber for, 81 



INDEX. 



523 



Feuder, 504 

pile, 215, 504 
Fernoline, 157 
Ferrolithic paving, 387 
Feno-manganese, 92, 111 
Field-rivets, 192 
Filling-piles, 215 
Fine-pointed stone. 237 
Fineness of cement, 39 

sieves for meas- 
uring, 39 
sand, to measure, 151 
Finishing-lumber, dimensions of yel- 
low pine, 83 
Fire-clay, composition of, 25 
Fire-brick, composition of, 25 
laying, 26 
qualities essential to good, 

26 
size of, 26 
weight of, 26 
Fire-proof construction, 504 

floors, 301 
Fishing, 280, 504 
Flagging, 388 

dressing of, 388 
Flange, 504 
Flash-boards, 504 
Flashing, roofs, 315, 505 
Flat-grain timber, 78 
Flat panels, 289 
Flatted, 295 
Flemish bond, 260 
Floor-beams, anchorage of, 283 

bearing of, 283 
Floors, brick arches, 301 
concrete, 305 

construction of fire-proof, 305 
fire-proof, 301 
hardwood, 282 
hollow-tile, 303 
laying tile, 305 
parts of, 283 
tests for tile, 305 
Flooring, centre-matched, 80 
common, 79 

dimensions of yellow-pine,83 
double, 282 
edge-grain. 79 
flat-grain, 79 
A-flat, 79 
B-flat, 79 

grade of common, 79 
laying, 282 
Flooring, rough yellow-pine, 82 
single. 282 
yellow-pine, 89 
Flume, 505 
Flush, 505 

joints, 265 
panels, 289 
tanks, 368 
Flux for asphaltum, 49 
Fluxes for soldering, 144 
Footings, 262 
Forge pig iron, 91 
Forging of iron &nd\ steel, 130 
Foundations, artificial, 211 
caissons, 211 



Foundations, care required to avoid 
fractures, 210 
clay, 210 
coffer dams, 212 
compressed-air process 

of sinking, 212 
cribs, 212 

duty of inspectors, 209 
freezing process for 

sinking, 212 
grillage, 213 
loads on, 211 
natural. 210 
pile, 214, 215 

plenum process of sink- 
ing, 212 
in rock, 210 
sand, 210 

vacuum process of sink- 
ing, 212 
Foundry pig iron, 91 
Foxiness in timber, 74 
Foxtail, 505 

Fracture of cast steel, 121 
rolled steel, 119 
stones, 16 
Frame, 505 
Freestone, 11 

Freezing process for sinking founda- 
tions, 212 
Frost, effect of, on brick, 25 

cement mortar, 40, 

247 
stone, 6 
test for effect on stone, 6 
Furrings, 505 
Fuse-blasting, 205 
Fusibility, 505 



Gain, 295 
Galvanized iron, 313 

manufacture of, 141 
Gasket, 505 

weight of, for pipe-joints, 363 
Gauge-pile, 215 
Gauge, wire, 162 
Gauged-work, 264 

Geological classification of stones, 4 
Giant powder, 205 
Gilsonite, 46 
Girder, 505 
Gin-pole, 505 
Glass, defects of, 338 

first and second quality, 338 

strength of, 338 

thickness and weight of, 339 " 
Glazed brick, 22 
Glazing. 339 
Glue, 159 

preparation of, 159 

test for, 159 

quality of, 159 
Gneiss, 9 

strength of ^Table 2), 13 
weight of (Tabh^ 2). 13 



524 



INDEX. 



Grade of ceiling-boards, 80 

flooring-boards, 79 

moulded casings and base, 

80 
timber, 77 
Grades of hardwood, 87 
Granite, absorption of, 6 

blocks, manufacture of, 371 

block paving, 371 

color of, 8 

decay of, 8 

defects of, 16 

dressing, 232 

description of, 8 

durability of, 8 

to detect presence of iron in, 
9 

inspection of, 16 

polishing, 233 

strength of (Table 2), 13 

weight of (Table 2), 13 
Granolithic paving, 387 
Gravel, description of, 152 
washing of, 152 
weight of, 152 
Greenstone, 9 
Grillage, 213 
Grit, 152 
Grout, 264 
Groove- joints, 266 
Grubbing, 506 
Guide-pile, 215 
Gum, 57 
Gussets, 506 
Gutters-roof, 315 
Guy, 506 

Gypsum, adulterant for Portland ce- 
ment, 41 

plaster of Paris, 154 



Halving, 280 

Hammer-beam, 286 

Hammer inspectors, 122 

Handrail, 288 

Handspike. 506 

Hardness, 506 

Hardening, 506 

wrought iron, 105 
of steel, 114, 130 

Hard pan, 198, 506 

Hardwood doors, 298 
floors, 282 

Haunches, 275 

Head-bay, 507 

Head -gate, 507 

Header in masonry, 264 
beam, 284 

Heading-joint, 275 

Heart-bond , 259 

Heart-shake in timber, 74 

Heat conductivity of cast iron, 95 
copper, 132 
lead. 134 
steel. 112 
tin, 136 



Heat conductivity of wrought iron, 102 
zinc, 141 
temperature of welding, 103 
Hemlock, 57 
Hemp, quality of, 160 
Hickory, 57 
Hip-roof, 506 
Hoarding, 506 
Hollow pile, 215 

quoin, 507 
Hornstone, 11 
Horse, 506 
Housing, 295 
Hydrants, inspection of, 365 

setting of, 365 
Hydraulic lime, 31 

limestone, 11 

proof of water-pipes, 356 
Hydraulicity of cement, 40 



Igneous rocks, 4 

Impost, 506 

Impurities in pig iron, 91 

Inches and equivalent decimals' of a 

foot, 394 
Incompetent workmen, dismissal of, 2 
Increase in bulk of excavated materi- 
als, 200 
Ingots, inspection of steel, 117 

marking steel, 118 
Inspection of asphalt paving, 382 

bolts and nuts, 184 

brick, 24 

masonry, 254 

broken -stone pavements, 
383 

carpentry, 279 

cast iron, 98 

pipes, 98, 354 

cement, 36 

concrete, 226 

cut stone, 241 

dredging, 207 

earthwork, 198 

foundations, 209 

granite- block paving, 372 

hardwood, 87 

hydrants, 365 

iron and steel, shop, 125 

lead pipes, 317 

lime, 31 

malleable cast iron, 100 

oak, 87, 88 

painting, 351 

piles, 221 

plastering, 336 

plumbing, 317 

riveting, 125,194 

rolled steel, 118 

roofing, 307 

rubble masonry, 252 

sand, 151 

sewer construction, 368 
pipes, 368 

spruce, 87 



INDEX. 



525 



Inspection of steel, 117 

ingots, 117 
pipe, 363 
stone, 16 

masonry, 253 
tiles, 28 
timber, 73 
treated timber, 69 
valves, 365 
varnishing, 352 
vitrified pipe, 366 
white pine, 86 
wrought iron, 104 
yellow-pine lumber, 83 
Inspector, duty of, 1 
Inspector's diary, 2 
report, 2 
shop records, 127 
Interpretation of specifications, 2 
Intrados, 275 
Invert, 275 
Iron, acid test for, 124 

appearance of good wrought, 104 
badly refined, 104 
bending test, cold, 105 
hot, 105 
blue-shortness, 131 
cast, 94 
checking and marking accepted 

pieces, 122 
cold rolling of, 129 

short, 104 
double refined, 101 
elongation of wrought, 103 
extraction from tl>e ore, 90 
forging of, 130 
galvanized, 141 
hardening wrought, 105 
in brick-clay, 18 

granite, 9 
inspection of cast, 98 

malleable cast, 100 
malleable cast, 100 
mill inspection of wrought, 104 
muck-bars, 101 

nicking and bending tests, 105 
notes on working, 129 
painting of, 352 
pig, 91 
piles. 216 
puddling, 101 
punching, 129 
red-short, 104 
refined, 101 
rivets, 195 

tests for, 105 
shearing, 129 

sheets, weight of (Table 19), 140 
shop inspection of, 125 
work records, 127 
size of test-pieces, 105 
straightening of, 125 
structures, erection of, 298 
test for rivet, 105 

pieces for cast, 98 
upsetting of, 131 
welding, 130 
wire, weight of, 165, 166 



Iron, wrought, composition of (Table. 
11), 102 
contraction of, 103 
elongation of, 103 
expansion by heat, 102 
extension of, 103 
manufacture of, 101 
modulus of elasticity, 

103 
properties of, 102 
reduction of area, 103 
specific gravity, 102 
strength of, 103 

welds, 103 
tenacity at high tem- 
peratures, 103 
to distinguish from 
other varieties, 102 
Ironstone, 11 



Jack, 506 
Jack-rafter, 286 
Jack-screw, 506 
Jag-bolts, 213 
Jam-nut, 506 
Jamb, 266 
Japanning, 350 
Jetty, 506 
Jib, 506 
Jim-crow, 506 
Joints in carpentry, 280 
masonry, 265 
Joists, 283 

bevelling ends, 283 
Joggle, 266 



Kalsomine, 350 
Kaolin, 153 
Kerf, 506 
Kerfed beam, 294 
Keys, 182 
Keyed joints, 265 
Keystone, 275 
Kiln -checks in timber, 76 
King-post, 286 
Knee, 506 
Knots in stone, 16 
Knot, standard, in timber, 77 
Knotty timber, 74 
Kosmocrete paving, 387 
Kyan's process for preserving timber, 
67 



Lafarge cement, 43 

Lag-screws, 180 

holding power of, 181 
size and weight of, 181 



526 



INDEX. 



1 



Laminations in relied steel, 119 

Laminated rocks, 5 

Lang-lay rope, 168 

Lap, 506 

Laps in rolled steel, 119 

Lapping, 280 

Lap- welding, 506 

Laths for plastering, 327 

Lead, 506 

cast, 134 

description of, 134 
expansion of, 134 
melting-point of, 134 
milled, 134 
pipe, 135 

pipes, inspection of, 317 
properties of, 134 
sheet, 134 
shrinkage of, 148 
specific gravity of, 134 
strength of, ^34 
waste-pipes, 317 
weight of, 134 

for cast-iron pipe- 
joints, 363 
sheet, 135 
Lift, 507 

wall, 507 
Lignum vitse, 58 
Lime, air-slaked, 31, 32 
in brick- clay, 18 
cubic feet in a barrel, 33 
excess in Portland cement, 34 
freshly burned, 31 
for plastering, 327 
hydrate of, 32 
hydraulic, 31 
inspection of. 31 
keeping slaked, 31 
market form of, 33 
poor, 31 
precautions to be observed in 

slaking, 32 
preservation of, 31 
properties of pure, 33 
putty, 328 
quality of, 31 
quick, 33 
rich, 30 
slaking of, 32 

sulphate of, plaster of Paris, 329 
stearate of, 331 
weight of, 33 
Limestone, 11 

bituminous, 48 
cherty, 11 
color of, 11 
compact, 12 
defects of, 16 
dolomitic, 12 
dressing, 234 
granular, 12 
hydraulic, 11 
inspection of, 16 
magnesian, 12 
oolitic, 12 
silicious, 11 

strength of (Table 2), 15 
weight of (Table 2), 15 



Limestones, absorption of, 6 
Limnoria terebrans, destruction of 

timber by, 66 
Line of cleavage, 4 
Lineal measure, 390 
Linings, 291, 506 

joints in, 291 
Linseed-oil, 343 
Lintels, length of bearing on walls, 300 

stone, 266 
Liquid measure, 391 
Listed, 294 
Lithocarbon. 47 
Live load, 507 
Load, 507 

Loam, composition of, 153 
Lock canal, 507 
Locks, setting door, 279 
Locust, 58 
Loose rock, 198 
Louvre, 507 
Lumber, 507 

centre-matched flooring, 80 
first and second clear flnish, 

78 
grade of fencing, 81 

flooring, edge-grain, 

flat-grain, B-flat, 

common flooring, 

79 

moulded casings 

and base, 80 
rough yellow-pine 

flooring, 82 
siding and grooved 
roofing, 79 
grades of ceiling, 80 
hardwood grades, 87 
oak flooring, 88 
partition, grade of, 80 
quality of dimension, 81 
rules for classifying, 76 

grading, common 

boards, 81 
grading, finished, 
78 
siding, grade of, 80 
standard dimensions of (flooFv 
ing, ceiling, finishing;^ 
boards, fencing, dimen- 
sion), 83 
standard lengths of^ 77 
third clear finish, 78' 
L5''Coris f ucata, 66 



M 

Macadam pavement, 883 

Machine-made brick, 20 

Magnesia in brick-clay, 18 

Mahogany, 58 

Malleability, 507 

Malleable cast iron, 100 

inspection of, 100 
strength of, 100 
iron, shrinkage of, 148 

Maltha, 46 

analysis of, 50 



INDEX. 



527 



Manganese, antidote for sulphur, 92 
bronze, 142 
effect on cast iron, 92 
steel, 93 

wrought iron, 93 
in Bessemer steel, 93 

brick-clay, 18 
steel, 114 
Manila hemp, test for, 160 
Manufacture, imperfect, of timber, 77 
right to require special 
methods, 2 
Maple, hard, 58 
white, 58 
Marble, 12 

dressing, 234 
dust for plastering, 328 
polishing, 235 
strength of (Table 2). 15 
weight of (Table 2), 15 
Marbles, absorption of, 6 
Marking rejected material, 1 
Marl, composition of, 153 
Masonry abutment, 259 

amount of mortar required 

for ashlar, 249 
amount of mortar required 

for broken ashlar, 250 
amount of mortar required 

for rubble, 251 
amount of mortar required 

for square stone, 250 
ashlar, 248 

backed with rubble, 

253 
facing, 242 
axed stones, 237 
batter, 259 
bond of, 259 

rubble, 251 
ashlar, 249 
brick (see Brick Masonry), 254 
broken ashlar, 250 
bush-hammered stone, 237 
classification of, 230 

the stones, 
230 
cleaning down, 260 
consistency of mortar for, 

246 
coping, 261 
coursed rubble, 251 
crandalled stone, 231 
cut stones, 237 
definition of courses, 262 

the terms used 
in, 259 
description of joints, 265 
detection of empty spaces in 

rubble, 252 
diamond-panel stone, 238 
drafted stones, 231 
dressing the stones, 231 
granite, 232 
limestone, 234 
marble, 234 
sandstone, 234 
effect of re-tempering mor 
tar, 247 



Masonry, fine-pointed stone, 237 

finishing faces of cut stone, 

237 
flushed joints, 242 
footing, 262 

general rules to be observed 
in laying all classes of, 253 
grout, 264 
header, 264 

inspection of rubble, 252 
joints in rubble, 251 
laying ashlar, 248 
lintels, 266 
methods of preparing the 

stones, 230 
mixing mortar, 243 
open joints, 242 
patched stones, 242 
pitched-faced stones, 231 
pean-hammered stone, 237 
pointing, 267 
proportions of ingredients 

foi- mortar, 245 
quality of mortar, 243 
quarry-faced stones, 231 
random -coursed rubble, 251 
repairs of, 258 
rip-rap, 268 
rock-faced stones, 231 
rough stones, 230 

pointed stones, 237 
rubbed stone, 238 
rubble, 251 

safe working loads for, 272 
sand for mortar, 245 
slope wall, 268 
stone-cutting, 231 
paving, 268 
stretchers in, 269 
squared stones, 230 
stone, 250 
tooth-axed stone, 237 
uncoursed rubble, 251 
unsquared stones, 230 
use of nigger-heads in rub> 
ble, 252 
spalls in rubble, 252 
Matched boarding, 296 
Maul, 507 
Material, marking rejected, 1 

removal of rejected, 2 
Materials produced from pig iron, 93 
tests for, 145 
testing strength of, 146 
Measures, 389 

comparing, 126 
miscellaneous, 392 
Measurement of timber, 73 
Melting-point of cast-iron, 95 

copper, ]32; lead, 134 
steel, 112 
wrought iron, 102 
zinc, 141 
Mensuration, 408 
Metals, extraction from ores, 90 
Metallithic paving, 387 
Metamorphic rocks, 4 
Metric measures, 392 
Metal, protection of, in fouudations,2H 



■ ■•■••■••■■■••■■aMMatitti 



528 



INDEX. 



Mica slate, 9 
Mill construction, 507 
3Iineral tar, 46, 157 
wool, 154 

weight of, 154 
Mitre, 281 

sill, 507 
3Iodulus of elasticity, 507 
Moisture, to determine amount in 

timber, 75 
Mortar, amount of cement and sand 
required for one cubic yard, 
249 
amount required for ashlar 

masonry, 249 
amount required for brick 

masonry, 256 
amount required for broken 

ashlar masonry, 250 
amount required for rubble 

masonry, 251 
amount required for square- 
stone masonry, 250 
colored, 257 
consistency of, 246 
effect of frost on, 247 

re-tempering, 247 
grout. 264 

lime for plastering, 327 
measuring the cement, 243 
mixing of, 243 
pointing, 267 
quality of, 243 
quantity of salt used, 248 
sand for, 245 
test for, 145, 246 
thickness of, in ashlar ma- 
sonry, 246 
thickness of, joints in brick 

masonry, 256 
use of salt in, 248 
water for, 245 
Mortise and tenon, 281 
Moulded panels, 289 
Mouldings, machine-wrought, 291 
planted, 290 
stuck, 291 
splicing of, 291 
Muck, 508 
Mucking, 508 
Muck-bars, iron, 101 



N 



Nails, 174 

composition, 174 

copper, 174 

cut, 174 

holding power, 174 

for plaster laths, 327 

wire, 174 

wrought, 174 
Natural stones, 4 

bed of stones, 5 
Neat lines, 508 

work, 508 
Newel, 288 
Nickel steej, 114 



Nicking and bending tests for iron, 105 
Nitroglycerine, 204 
Nomenclature of asphaltum, 47 
Nosing, 288, 508 
Notching, 281 
Nuts, 184 



O 

Oak, chestnut, 59 
live, 59 

red and black, 59 
white, 59 

inspection of, 87, S 
quartered, 88 
rift-sawed, 88 
One-man stone, 266 
Open-hearth steel, 110 
Origin of bitumen, 45 
Out of square, 508 
wind, 508 



Paints, asphalt, 346 

bituminous, 346 
coal-tar, 346 
graphite, 347 
metallic, 347 
special, 346 

test for water-proof, 352 
Putty, 350 
Painting, 340 

adulteration of red lead, 342 
white lead, 
341 
bases, 340 
benzine in, 344 
fillers, 353 
inspection of, 351 
iron, 352 
Joplin lead, 341 
knotting, 351 
linseed-oil, boiled, 343 
raw, 343 
adulteration of, 

344 
substitutes for, 
344 
materials employed for, 340 
naphtha, 344 
oxide of iron, 343 
oxysulphide of zinc, 342 
pigments, 344 
black pigments, 344 
blue pigments, 345 
brown pigments, 345 
green pigments, 345 
red pigments, 345 
yellow pigments, 3-16 
plaster, 351 
priming-coat, 351 
proportion of ingredients, 

346 
red lead, 342 
solvents, 344 
Stainers, 344 



INDEX. 



539 



Painting, sublimed lead, 341 

sulphate of baryta, 341 
tin, 352 

turpentine, 344 
vehicles for, 343 
Vermillion, 343 
white lead, 340 

adulterations of, 

341 
tests for, 341 
wood, 351 
zinc white, 342 
Pallets, 268 
Palmetto, 59 
Panelling, 289 

varieties of, 28S 
Pan-tiles, 28 
Paper sheathing, 158 
Parapet wall, 266 
Paving, asphalt, 374 

laying of, 381 
preparation of, 381 
artificial stone, 387 
bituraincas limestone, 375 

sandstones, 375 
brick pavement, 385 
characteristics of brick, 385 
curbstones, 388 
flagging, 388 
granite blocks, 371 
inspection of asplialt, 382 
brick, 385 
granite-block, 

372 
macadam, 383 
Telford, 383 
laying brick, 386 
macadam, 383 
materials employed for, 371 
paving-pitch, 156, 373 i 

properties of brick, 387 
size of brick, 387 
Telford, 383 
tests for brick, 145, 385 
tiles, 28 

Trinidad asphaltum, 376 
wood paving, 374 
Pean-hammered stone, 237 
Perpend bond, 259 
Petrolene, 44 
Phosphor bronze, 142 
Phosphorus, effect of, on cast iron, 92 
on steel, 92 

wrought iron, 92 
Physical classification of stones, 4 
Piers, bond-stones in, 260 
Pig, 508 

iron, classification of, 91 

composition of (Table 8), 91 
impurities in, 91 
materials produced from, 93 
Pile, 508 

caps, 213 
close, 215 
driving, 218 

excessive hammering, 218 
heavy or flight hanuner 

for, 218 
machines, 219 



Pile driving, record, 221 

steam-hammer for, 2i9 
use of follower, 219 
water- jet for, 219, 
Piles, anchor, 215 

bands for, 218 
bearing, 215 
bouncing of, 218 
brooming of, 218 
cast-iron, 216 
description of, 215 
disk, 215 
false, 215 
fender, 215 
filling, 215 
gauge, 215 
guide, 215 
hollow, 215 
inspection of, 221 
iron and steel, 216 
pneumatic, 216 
pointing of, 214 
sand, 216 
screw, 216 
sheet, 216 
short, 217 
splicing of, 221 
steel, 216 
test, 217 
timber for, 214 
Pilot- nut, 508 
Pins, 182 

tests for, 145 
Pipes, inspection of cast-iron, 9S 
Pine, white, inspection of, 86 
white, 59 
red, 60 
yellow, 60 
Oregon, 60 
long-leafed, 60 
short-leafed, 60 
Pitch-streaks, 76 
Pitched -faced stones, 231 
Pitch of rivets, 190 
Plant, 508 

Planted moulding, 291 
Plaster of Paris, 154, 329 

painting of, 351 
Plastering, area covered with one 
cubic foot of cement and sand, 
335 
Plastering, brown coat, 324 
classes of, 323 
coarse stuff, 324 
cornice, 325 
dots, 325 
dubbing out, 325 
fine stuff, 325 
finishing coat, first coat, 

325 
floated lath and plaster, 
floated work, floating- 
screeds, 325 
furring, 325 
gauge-stuff, 325 
grounds, 326 
hair for. 326 
liMtid tloaiiii};, 320 
hard llnish, 326 



IlllllllllllllllilillllllJ 



530 



INDEX. 



Plastering, inspection of, 336 

Keene's cement, 326 
laid and set. 326 
laths for. 327 
wood. 327 
metallic, 327 
laying, 327 

(see Scratch-coat), 
3:30 
lime for, 327 
mortar, 327 
putty, 328 
marble-dust for, 328 
material used for, 323 
mixing lime mortar, 328 
nails for laths, 327 
one-coat work, 329 
parqetting, 329 
plaster of Paris, 329 
pugging, 329 

quantity of materials re- 
quired per square yard, 
335 
rendering, 329 
roughcast, 329 
rule, 329 
sand for. 329 

finish, 330 
Scagliola, 330 
scratch-coat, 324, 330 
screeds, 331 
screed-coat, 324 

and set, 331 
skim-coat, 331 
slipped-coat, 324, 331 

stucco, common, 

332 
bastard, 332 
trowelled, 332 
tile arches, 337 
tools used in, 333 
two-coat work, 333 
three-coat work. 333 
weiglit of hair, 326 
white coating, 333 
Plate, 296 
Phability, 508 
Plinth-course, 262 
Plough-groove, 296 
Plumbing, air test, 322 

inspection of, 317 
peppermint test, 321 
smoke test, 321 
tests for, 321 
water test, 321 
Pneumatic piles, 216 
Point, steel working, 116 
Pointing masonry, 267 
Polishing granite, 233 
marble, 235 
Pony-truss, 448 
Poplar, 61 

inspection of, 87 
Portland cement, 34 

adulteration of, 35 
blowing and swell- 
ing of. 3") 
clay in, 34 
color of, 34 



Portland cement, characteristics of, 34 
composition of, 34 
excess of lime in, 34 
expansion and con- 
traction of, 34 
fineness of, 34 
overlimed, 35 
quality of, 34 
underburnt, 34 
setting of, M 
specific gravity of ,34 
tensile strength of ,34 
weight of, 34 
Pozzuolana, 43 
Pressed brick, 20 
Preservation of cement, 38 
stone, 7 
timber, 66 

process for, 
67, 68 
Preserving timber, form of report, 70 
Primed, 508 

Processes for preserving stone, 7 
Processes for preserving timber — 
Kyan's, Burnett's, Brucheris', Beth- 
el's, Payne's, Seeley 's, Wellshouse's, 
Thilmany's, vulcanizing, 67, 68 
Profile, 508 
Proof load, 508 
Properties of steel, 112 

timber (Table 7), 56 
zinc, 141 
Puddled steel, 109 
Puddling clay, 223 
iron, 101 
Purlin, 286 



Q 

Quartered oak, 88 
Quarry-faced stones, 231 
Quarrying. 17 
Queen -post, 286 
Quicksand, 508 
Quoin, 268 



Rabbet, 296 
Racked-back, 508 
Rafter, 286 
Rails, tests for, 145 

door, 289 
Raked out, 508 
Ramp, 508 
Ransome's process for preserring 

stone, 7 
Rebate, 296 

Recalescence of steel, 116 
Red lead, 342 

adulteration of, 342 
heart, 77 
Redwood. 61 
Refuse, timber, 87 
Refined iron, 101 
I Rejected material, marking, 1 



INDEX. 



&31 



Rejected material, removal of, 2 
Repairs of masonry, 258 
Report of iuspectors, 2 
Repressed brick, 20 
Residuum oil, 51 

specifications for, 51 
test for, 51 
Resilience, 509 

Requisites for good building stone, 5 
Retme, 45 
Return, 508 
Reveal, 268, 509 
Ribs in slate, 11 
Ridge, 286 
Ridge-beam, 286 
Rift-line in rocks, 4 
Rift-sawed oak, 88 
Ring course, 276 
Ririg-heart in timber, 76 
Rind-gall in timber, 74 
Rip-rap, 268 
Rise, 268, 276 

of stairs, 288 
Riser, 288 
Rivet-holes, 194 
Rivet-iron, test for, 105 
Rivet signs, 192 
Rivets, button-headed, 190 
calking of, 193, 196 
cold, 196 

countersunk, 190 
cup-ended, 190 
description of, 188 
detection of loose, 196 
field, 192 
form of, 190 
hammered, 190 
heating of, 195 
iron, 195 
length of, 188 

required to form head, 
188 
loose, 196 

marking defective, 197 
pitch of, 190 
precautions to be observed 

with steel, 195 
redriving, 196 
size of, 188 
Rivets, steel, 195 

tests for, 145, 194 
weight of, 191 
Riveting, 192 

chain, 190 
cold, 193 
double, 190 

essentials of good, 194 
field. 126 
hand, 192 

inspection of, 125, 194 
machine, 193 

pressure required for, 193 
quadruple, 190 
single, 190 
staggered, 190 
triple, 190 
use of drift-pin, 12G 
zigzag, 190 
Rock-blasting, ;J04 



Rock-drilling, 203 

hand, 203 
machine, 203 
Rock excavation, 203 

foundations on, 210 
Rocks, cleavage line or rift of, 4 
dikes in, 5 
igenous, 4 
laminated, 5 
metamorphic, 4 
sedimentary, 4 
stratified, 4 
unstratified, 4 
Rock-faced stones, 231 
Rolled steel, inspection of, 118 
Roman brick, 23 

cement, 43 
Roof-flashing, 315 
Roof-framing, 286 
Roof-gutters, 315 
Roof, parts of, 286 
valleys, 315 
Roofing-boards, 79 
Roofing, copper, 314 

galvanized iron, 313 
inspection of, 307 
laying shingle, 309 
slate, 309 
tile, 308 
tin, 308 
materials, weight of, 314 
sheathing-boards, 307 
slate, 309 

manufacture of, 235 
tiles, 28 
tin, 307 
Roofs, 286 
Rope, 160 

hemp, 160 
manila, 160 
strength of, 161 
Rosendale cement, 35 

characteristics of, 

35 
color of, 35 
specific gravity of, 

35 
strength of, 35 
underburnt, 35 
weight of, 35 
Rosin-paper, 158 
Rot in stone, 16 
Rotten-stone, 11 
Rotten-streaks in timber, 76 
Rough-pointed stone, 237 
Rowlock course, 262 
Rubbed stone, 238 
Rubble masonry, 251 
Rules for grading finished lumber, 78 



Saddle-heads, 509 

Salt in cement-mortar, 40 

Salt, quantity used in mortar, 248 

Sampling cement, MO 



fiiiiiiiiiiifiiifiiiinni 



532 



Iiq"DEX. 



Saud, arf?illaceous, 150 
calcareous, 150 
coarse. 151 
definition of, 150 
fine, 151 
for plastering, 329 

mortar, 245 
in brick-clay, 18 
measuring fineness of, 151 
method of drying, 152 
method of washing, 152 
mixed, 151 
piles, 216 
pit, 150 
river, 150 
sea, 150 

screening of, 152 
sharp, 245 

sieves for measuring fineness, 151 
siliceous, 150 
size of, 151 

testing cleanness of, 151 
for clay, 151 
salt, 151 
sharpness of, 151 
use of, 150 
voids in, 151 
weight of, 151 
Sandstones, 10 

absorption of, 6 
bituminous, 48 
color of, 10 
decay of, 10 
defects of, 10 
dressing, 234 
durability of, 10 
inspection of, 16 
scaling of, 10 
seasoning of, 10 
setting on natural bed, 10 
strength of (Table 2), 14 
weight of (Table 2), 14 
Sap in stone, 16 
Scaffold, 509 
Scagliola, 330 
Scantling, 296 
Scarf, 296 
Scarfing. 280 
Scow, 509 
Screw-piles, 216 
Screws, description of, 180 
lag, 180 
for metal, 182 
size of wood, 180 
Scribe. 509 
S(;ril)iiig. 296 
Seasoned, 296 

Seastmiiig checks in timber, 76 
of stone, 17 
of timber, 62 

time required for, 
62 
Secants (Table 83), 472 
Secrer-nailed, 282,296 
Spdinientary rocks, 4 
Sefifiegation of steel, 117 
^(M>MrnfO!-s, 509 
St. 5(H) 
beUiiig of cement, 41 



Sewer-pipe, length that one barrel of 

cement will lay, 370 
Sewerage, brick sewers, 369 

concrete or cement pipes, 

367 
flush tanks, 368 
inspection of construction, 
368 

pipes, 368 
vitrified pipe, 
366 
lamp-holes, 368 
laying vitrified pipe, 367 
manholes, 368 
materials employed for, 366 
pipe sewers, 368 
tests for pipe, 367 
vitrified pipe, 366 

weight of, 
370 
Shaft, 509 
Shakes in stone, 16 
Shake in timber, 76 
Shackle, 509 
Shear-steel, 109 
Shearing stress, 509 
Sheathing-felts, 158 

papers, 158 
Sheet-piling, 216, 217 
Shim, 509 
Shingle, 152 

roofs, 309 
Shingles, number per square, 309 
requisites for good, 309 
weight of, 309 
Ship-lap, grade of, 81 

material, tests for, 145 
Shop records, 127 
Shoes, 509 
Shoot, 509 
Shore, 509 
Shot, 296 
Shrinkage of cast iron, 96 

excavated materials, 200 
metals, 148 
steel castings, 121 
timber, 63 
Siding, grade of, 80 
Siemens-Martin steel, 110 
Sieves, size of, for measuring fineness 

of cement, 39 
Silicon, effect on cast iron, 93 
steel, 93 

wrought iron, 93 
Silicious stones, 5, 8 
Sill, 268, 296 
Silt, 509 

Sines, tangents, secants (Table 83) 463 
Sinking, 509 
Siphon culvert, 509 
Sisal hemp, test for, 161 
Size of bricks, 23 

tin roofing-plate, 137-139 
wire, 162 
Skeleton construction, 510 
Skew-back, 276 

bncks, cutting of, 232 
Skid, r'O'.) 
Slag cemenl, 42 



INDEX. 



533 



Slaking lime, 32 
Slate, 11 

Slate, color of, 11 
dressing ,235 

raanufacture of roofing, 235 
number per square, 312 
ribs in, 11 
roofing, 309 
tests for roofing, 311 
veins in, 11 

weight of (Table 2), 14 
Slates, characteristics of good roofing, 
311 
gauge of, 310 
notes on roofing, 311 
Slings, 510 
Slips, 268, 510 
Slip-joint, 258 
Slopes of earthwork, 199 
Slope-wall, 268 
Sluice, 510 
Smith's coating for cast-iron pipes, 

355 
Sodding, 510 
Soffit, 275 

Soft metals, tests for, 145 
Soils, bearing power of, 211 
Soil-pipe, cast-iron, 320 
Solders, 144 
Solid rock, 198 
Solvents for asphaltum, 44 
Soundness of cement, 41 

stone, to test, 16 
Spall, 268, 252 
Span, 276 
Spandrel, 276 

beam, 510 
Special methods of manufacture, 

right to require, 2 
Specific gravity, 396 

of asphaltum, 44 
\nck (Table 4), 

23 
lead, 134 
materials, 396 
Portland cement, 

34 
Rosendale cement, 

35 
steel, 112 
Specific gravity of tin, 136 

wrought iron, 102 
zinc, 141 
Specifications for cast steel, 121 

failure to comply with, 

3 
interpretation of, 2 
Spiegel, 92 
Spiegeleisen, 92, 111 
Spile, 510 
Spillway, 512 
Splay, 510 . 

Splice, 296, 510 
Spline. 296 
Splits in timber, 74 
Springing, 278 

course, 262 
Spruce, black, 61 
white, 61 



Spruce, inspection of, 87 
Square measure, 390 

roots, 416 
Stage, 510 
Stains, 350 

Stairs, construction of, 287 
Standard knot in timber, 77 
Standing finish (carpentry), 290 
Star-shake in timber, 74 
Starling, 262 
Steel, acid process, 110 
test for, 124 
alloys, 114 
annealing, 129 

appearance and characteristics 
of good, 117 
of fracture of 
rolled, 119 
basic process, 110 
bending test, cold, 123 
hot, 122 
Bessemer and open-hearth. 111 

process, 110 
bled ingots, 115 
blister, 109 
blowholes in, 117 

rolled, 118 
blue-shortness, 131 
burned, 115 
calking of joints, 131 
carbon in, 112 
cast, 111 

appearance of fracture, 121 
tests for, 121 
castings, 121 
checks in, 115 
checking and marking accepted 

pieces, 122 
chemical numeration of, 115 
chrome, 115 

cinder-spots in rolled, 119 
classification of, HI 
cobbles in rolled, 119 
cold-short, 116 

rolling of, 129 
color of rolled, 119 
composition of, 109 
compressed, 115 
contraction of, 112 
cracks in rolled, 119 
dead melting, 115 
drifting test, 123 
dry, 118 

effect of manganese on, 93 
phosphorus on, 92 
silicon on, 93 
sulphur on, 92 
expansion of, 112 
external cracks in, 117 
extension of, 112 
facing and boring, 126 
fire-box, 112 
fiery, 118 
flange, 111 
for boilers, 120 
forging of, 130 
for-ging, test for, 123 
form of inspector's marking- 
tool, 122 






534 



INDEX. 



Steel, form of test-billet, 118 
fracture of burned, 120 
grade of, 115 
hard. 111 

strength of (Table 14), 113 
hardening of, 114, 130 
soft, 129 
tests for, 123 
heat or blow tests, 118 
homogeneity test, 124 
hot-short, 116 
inspection of ingots, 117 

riveting, 125 
internal cracks in, 117 
laminations in, 119 
laps in rolled, 119 
loading on cars, 128 
manganese, 114 
manufacture of, 109 
marking of ingots, 118 
medium. 111 

strength of (Table 14), 
113 
melting-point, 112 
melt records, 118 
mild, 111 

mill inspection of, 117 
nickel, 114 

notes on working, 129 
overblown, 115 
overheated, 115 
overmelted, 116 
piles, 216 
pipe in, 117 

rolled, 118 
pipe, coating for, 364 
pipe, inspection of, 363 
pits in rolled, 119 
point, term in working, 116 
properties of, 112 
puddled, 109 
punching, 129 
tquenching test, 124 
recalescence of, 116 
red short, 116 
restoring of, 116 
rivets, 195 

rolled, inspection of, 118 
rough handling of, 129 
sappy, 117 
segregation of, 117 
seams in rolled, 119 
shear, 109 
shearing, 129 
shell. 111 
shop inspection of, 125 

records, 127 
shrinkage of, 148 

castings, 121 
Siemens-Martin's process, 110 
Siemens or open-hearth pro- 
cess, 110 
soft. 111 

strength of (Table 14), 
113 
snakes in rolled, 119 
specific giaviiy, 112 
specifications for cast, 121 
Stars in rolled, 118 



Steel, straightening of, 125 
strength of, 112 

welds, 114 
structures, erection of, 298 
tank, 111 
temper of, 116 

temperature of working indica- 
ted by fracture, 119 
tempering of, 130 
tenacity at high temperatures, 

113 
tensile tests, 122 
terms used in working, 115 
tests for, 122 

to distinguish from iron, 109 
tungsten, 115 
upsetting of, 131 
use of di ift-pin in riveting, 126 
varieties of, 109 
water-cracks in, 116 
weight of, 112 
welding of, 130 

test for, 123 
wild, 116 

wire, weight of, 165, 166 
Stiffness, 510 
Stiles, 289 
Stirrup, 511 
Stone, absorptive power of, 6 

argillaceous, 5, 11 

artificial, composition of 29 

basalt, 9 

boat, 510 

calcareous, 5, 11 

cavities in, 16 

chemical classification, 5 

classification of, 4 

crowfoots in, 16 

cut, 231 

drafted, 231 

dry sin, 16 

durability of, 5 

effect of atmosphere on, 7 
frost on, 6 

fracture of, 16 

freestone, 11 

geological classification, 4 

gneiss, 9 

granite, 8 

greenstone, 9 

inspection of, 16 

knots in, 16 

laminae or beds of, 5 

limestone, 11 

marble, 12 

mica-slate, 9 

natural, 4 

bed of, 5 

paving, 268 

physical classification, 4 

pitched-faced, 231 

powder-cracks in, 17 

preservation of, 7 

quarry-faced, 231 

quarrying, 17 

Ransome's process for pre- 
serving. 7 

requisites for good building, 5 

rock-faced, 231 



INDEX. 



535 



stone, lot in. 16 

rough-pointed, 237 
rubbed, 238 
sandstones, 10 
sap in, 16 
seams in, 16 
seasoning of, 17 
shakes in, 16 
siliceous, 5, 8 
squared, 230 
test for, 6, 145 

effect of atmosphere 

on, 7 
frost, 6 

soundness of, 16 
tooth-axed, 237 
trap, 9 

unsquared, 230 
veins in, 16 
weather-worn, 17 
syenite, 9 
atone-cutting, 231 

arch-stones, 232 
ashlar facing, 242 
axed stone, 237 
beds and joints, 231 
bush-hammered stone, 

237 
chisel draught, 231 
concave beds, 241 
crandalled stone, 237 
diamond-panel stone, 

238 
fine-pointed stone, 237 
granite, 232 
inspection of, 241 
limestone, 234 
marble, 234 
method of finishing 

the face, 237 
patched stones, 242 
patent hammered 

stone, 237 
pean-hammered stone, 

237 
rough - pointed stone, 

237 
rubbed stone, 238 
sandstone, 234 
slack beds, 241 
slate, 235 

terms used in, 240 
tooth-axed stone, 237 
tools used in, 238 
Storing cement, 38 
Strain, 450 
Straining-beam, 287 
Stratified rocks, 4 
Strength, 510 

of bolts, 187 

brick (Table 4), 23 
cable chains, 173 
cast iron, 96 
cement, 41 
concrete, 224 
copper, 132 
fiat wire ropes, 171 
tile arches, 304 
galvanized wire rope, 171 



Strength, of granite (Table '<?), 13 
iron wire rope, 109 
glass. 338 
lead, 134 

limestone (Table 2), 15 
malleable cast iron, 100 
manila rope, 162 
marble (Table 2), 15 
Portland cement, 34 
Rosendale cement, 35 
sandstone (Table 2), 14 
steel, 112 

cables, 172 
rope, 170 
terra cotta (Table 5), 27 
timber (Table 7), 57 
tin, 136 

trap (Table 2), 13 
welds, wrouglit-iron, 103 
wire, 167 

wrought iron, 103 
zinc, 141 

Stress, 510 

Stretching course, 26? 

String course, 262, 269, 276 

Strings, 288 

Stringer, 296, 511 

Struck joints, 265 

Struts, 287. 511 

Stuck-moulding, 291 

Stud, 296, 511 

Stud-bolt, 511 

Sulphur, effect on cast iron, 92 
steel, 92 
wrought iron, 92 

Sump, 511 

Swedged, 511 

Swivel, 511 

Syenite, 9 

strength of (Table 2), 13 
weight of (Table 2), 13 

Sylvester's washes for brick masonry, 
257 



Tail-bay, 283, 507 

gate, 507 
Tamp, 511 

Tangents (Table 85), 487 
Tap-bolt, 511 
Tar-felt, 158 
Tarred paper, 158 
Telford paving, 383 
Temperature of welding heat, 103 
Tempering, 511 

asphaltum, 49 

steel, 130 
Temper, term in steel working, 116 
Templets, 269,511 

Tenacity of cast iron at high tempera- 
tures, 96 
Tenacity of steel at high temperatures, 

Tenacity of wrought iron at high toni- 

l)eratiires, 103 
Tension. 511 
Ten-do navalis, 65 



TWTWWmMlMrail 



536 



INDEX. 



TereJo navalis, destruction of timber 

by, 65 
Terms used in carpentry, 293 
masonry, 259 
stone-cutting, 240 
steel working, 115 
Terra-cotta, defects of, 26 

description of, 26 
porous, 28 
specimens : 
for compression tests, 
148 
impact tests 148, 
tension tests, 146 
transverse tests, 148 
size of, 146 
strength of (Table 5), 27 
weight of, 27 
Test-pieces, proportions of, 146 

piles, 217 
Tests for asphaltum, 52 

bituminous rock, 53 
brick, 24 
cast-iron pipe, 355 

steel, 121 
cement, 37 
copper, 132 

effect of atmosphere on 
stone, 7 
frost on stone, 6 
glaze of vitrified pipe, 366 
glue, 159 
hydraulic, for pipes, 356 
for iron in granite, 9 
rivets, 105 
Manila hemp, 160 
materials, 145 
mortar, 246 
paving-brick, 385 
pipe-coatings, 364 
plumbing, 321 
puddle clay, 223 
residuum oil, 51 
rivets, 194 
roofing-slate, 311 
sand, 151 
sewer-pipe, 367 
sisal hemp, 161 
slag cement, 43 
soundness of stone, 16 
steel, 122 
stone, 6 
tile floor, 305 
timber, 74 

treated with zinc 
• chloride, 69 
tin, 136 

roofing-plate, 137 
water-proof paint, 352 
water-pipes when laid, 358 
white lead, 341 
wrought iron, 105 
speed for applying tensile, 146 
tensile, precautions to be ob- 
served in, 146 
Testing-machine, 146 

stretigth of materials, 146 
Tie-beam, 287 

rods for brick arches, 302 



Tile floors, 303 
Tiles, description of, 28 
encaustic, 28 
flat, 28 

inspection of, 28 
pan, 28 
paving, 28 
roofing, 28, 308 
weight of, 28 
Timber, absorptive power of. 75 
appearance of good, 73 
artificial seasoning of, 62 
ash, description of, 56 
blue sap in yellow pine, 76 
bright sap in yellow pine, 77 
cedar, description of, 56 
common rot in, 65 
creosoting of, 67 
culls, 87 

cypress, description of, 57 
defects of : wind-shakes, 
splits, checks, cracks, 
brash, belted, knotty, 
twisted, heart-shake, cup- 
shake, rind gall, upset, 
foxiness, doatiness, 74 
defects in rough stock, 77 
destroyed by Teredo navalis, 
65 
Limnoria tere- 
brans, 66 
dressed yellow pine, 82 
dry rot in, 64 

detection of, 65 
durability and decay of, 64 
edge-grain, 77 
elm, description of, 57 
expansion by heat, 64 

of , by water, 63 
flat-grain, 78 
flat-sawed, 88 
for piles, 214 
grade of, 77 
gum, description of, 57 
hemlock, description of, 57 
hickorj', description of, 57 
imperfect manufacture, 77 
inspection of, 73 

hardwood, 87 
spruce, 87 
treated, 69 
white pine, 86 
yellow pine, 83 
kiln-checks in, 76 
kinds of, 55 
lignum vitae, description of, 

58 
locust, description of, 58 
(lumber) first and second 
clear finish, 78 
rules for classify- 
ing, 76 
rules for grading 

finished. 78 
standard lengths, 77 
mahogany, description of, 58 
maple, description of, 58 
measurement of, 78 
natural seasoning of, 62 



INDEX. 



537 



Timber, oak, description of, 59 

palmetto, description of, 59 
pine, description of, 59 
pitch-streaiis in yellow pine, 

76 
poplar, description of, 61 
preservation of, 66 
preservative processes for : 
Kyanizin^, Burnettizing, 
Boucheri's, Bethel's, 
Payne's, Seeley's, Wells- 
house's, Thilmany's, vul- 
canizing, 67, 68 
preserving, form of report, 70 
properties of (Table 7), 56 
quarter-sawed, 88 
redwood, description of, 61 
resistance to cross-breaking, 
57 
crushing, 57 
shearing, 57 
tension, 57 
rift-sawed, 88 
rotten-streaks in, 76 
rough yellow pine, 82 
seasoning of, 62 

checks in, 76 
shrinkage of, 63 
spruce, description of, 61 
standard knot, 77 
strength of (Table 7), 57 
strip count, 78 
structure of, 55 
test of, 74 

for, treated with zinc 
chloride, 69 
time required for seasoning, 

63 
to determine amount of 

moisture in, 75 
walnut, description of, 61 
wane in, 76 
water-seasoning of, 62 
weight of, 57 
wet, rot in, 65 
worms in, 65 

(yellow pine) defects of, 76 
Tin, bright, 137 

description of, 136 

expansion of, 136 

painting of, 352 

poperrties of, 136 

roofing, 307 

specific gravity of, 136 

strength of, 136 

terne plate, 137 

tests for, 136 

weight, 136 

plate, manufacture of, 137 

roofing-plate, 137 

quality of, 137 
size of sheets, 137 
thickness of, 137 
weight of, 139 
shrinkage of, 148 
Tires, tests for, 145 
Thickening washers, 511 
Thilmany's process for preserving 
timber, 67 



Thimble, 512 
Through bond, 259 

bridge, 512 
Tongue, 296 

Tools used in stone-cutting, 238 
Tooth-axed stone, 237 
Toothing, 269 
Torsion, 512 
Transom, 297 
Transverse strength of timber, 57 

stress, 512 
Trap, 9 

strength of (Table 2), 12 
weight of (Table 2), 13 
Tread, 289 
Trenails, 182 

Trigonometrical functions, 461 
Trim (carpentry), 290 
Trimmer-beams, 284 
i Trimming, 284-287 

rules governing, 284 
Trinidad asphaltum, 376 

cheese pitch, 376 
fipuree, 376 
iron pitch, 376 
land pitch, 376 
Truss, 512 

beam, 294 
Tuck pointing, 267 
Tungsten steel, 115 
Turn buckle, 512 
Twisted timber, 74 
Two-men stone, 269 



U 

Uintahite, 46 
Underpinning, 512 
Unstratified rocks, 4 
Upright, 297 
Upset, 512 

in timber, 74 
Upsetting, steel and iron, 181 



Valley, 512 
Valleys, roof, 315 
Varieties of cast iron, 94 

steel, 109 
Varnish, 348 

asphalt, 349 
quality of, 348 
Varnishes, oil, 348 

spirit, 349 
water, 349 
Varnishing, inspection of, 352 
Veins in slate, 11 
Veneered, 297 
Vitrified pipe, 366 

inspection of, 366 
salt glaze, 366 
slip glaze. 366 
test for glaze, 366 
tests for. 367 
Voids in broken stone, 384 

sand, 151 
Voussoirs, 276 



llllllllllllliiiiiiiiiTTrnH 



538 



INDEX. 



Vulcanizing timber, 68 



W 

Wainscoting, 291 
Wales, 512 

Walls, anchoring, 269 
bracing, 270 
curtain, 270 
furred, 270 
plates, 287 
recesses in, 270 
thickness of, 271 
Walnut, black, 61 
white, 61 
Wane in timber, 76 
Warp in timber, 76 
Warped, 512 
Washers, 513 

size and weight of, 184-187 
Washboards, 297 
Waste-weir, 512 
Wasted, 512 
Water for mortar, 245 

jet for driving piles, 219 
pipes, examining cast-ii on, 98 
supply, back-filling trenches,359 
cast-iron pipes, calking 

joints of, 357 
cast-iron pipes, coating 

of, 355 
cast-iron pipe, Barff's 

coating for, 356 
cast-iron pipe, Doctor 
Smith's coating for, 
355 
cast-iron pipes, defects 

of, 354 
cast-iron pipes, gasket 

for joints of, 357 
cast-iron pipes, inspec- 
tion of, 354 
cast-iron pipes, la3'^ing 

of, 357 
cast-iron pipes, lead 

for joints, 363 
cnst-ij'on pipes, tests 

for, 355 
cast iron pipes, weight 

of, 300 
hydrants, inspection 

of, 365 
hydrants, setting of, 

365 
hydraulic proof of, 

pipes, 356 
materials employed 

for, 354 
steel pipe, 363 

coating for, 

364 
inspection 
of, 363 
steel pipe, laying of, 

364 
test for pipe-coating, 
364 



Water-supply, testmg pipes after lay- 
ing, 358 
tools used in calking, 

358 
valves, inspection of, 
365 
setting of, 365 
weight of lead and 
gasket for cast-iron 
pipes, 363 
weight of standard 
specials, 362 
Water-table, 262 
Weather-boarding, 297 

joint, 265 
Wedges, 182 

Weight of brass sheets (Table 16), 133 
wire (Table 16), 133 
bricks, 23 

per cu.ft. (Table 4),23 
broken stone, 384 
cast iron, 95 

soil-pipe, 320 
casting from weight of pat- 
tern, 149 
cements, 38 
concrete, 224 
copper, 132 

sheets (Tablel3),133 
wire (Table 16), 133, 
165 
flat tile arches, 304 
fire-brick. 26 
galvanized iron, 313 
gasket for pipe- joints, 363 
glass, 339 

gneiss (Table 2), 13 
granite (Table 2), 13 
gravel, 152 
hair, 326 
hollow brick, 23 
iron wire, 165 
lag-screws, 181 
lead, 134 

waste pipe, 317 
lime, 33 

limestone (Table 2), 15 
marble (Table 2), 15 
materials (Table 80), 396 
mineral wool, 154 
paving-brick, 387 
Portland cement, 34 
rivets, 191 

roofing materials. 314 
round copper (Table 15), 132 
Rosen dale cement, 35 
salt-glazed sewer-pipe, 370 
sand, 151 

sandstone (Table 2), 14 
sheet iron (Table 19), 140 

lead, 135 
shingles, 309 
slate (Table 2), 14 
steel, 112 

wire, 165 
terra-cotta, 27 
tiles, 28 
timber, 57 
tin. 136 



INPEX. 



539 



Weight of tin roofing- plate, 139 
trap (Table 2), 13 
washers, 187 
wood, 56 

wrought-iron nails, 175 
zinc, 141 
Weights and measures, 389 
Weir, 512 
Weld, 512 

strength of steel, 114 

wrought iron, 103 
Welding heat, temperature of, 103 
iron, 130 
steel, 130 
wrought iron, 102 
Wellshouse process for preserving tim- 
ber, 67 
Wet rot in timber, 65 
Whitewood, 61 

White lead, adulteration of, 341 
tests for, 341 
skate-joint, 266 
Whitewash, 350 
Whiting, 350 
Wind, 512 
Winder, 289 

Windows, construction of, 292 
Wind-shakes in timber, 74 
Wing-walls, 512 
Wire, 162a 

gauge, U. S. standard, 164 
gauges, 162 

compared, 163 
nails, 174 

number of yards of, to the bun- 
dle, 167 
strength of, 167 
rope, 168 

tests for, Ho 
tests for, 145 
weight of, 165 

brass (Table 16), 133 
copper (Table 16), 133 
Workmen, dismissal of incompetent, 2 
Wood, absorptive power of, 75 
bricks, 269-297 
creosote, 157 

description of (Table 7), 56 
painting of, 351 
paving, 374 
screws, size of, 180 
tar, 157 
tests for, 145 
weight of, 56 
Woodiline, 157 
Worms in timber, 65 
Wrought iron, composition of (Table 
11), 102 
distinguished from 

other varieties, 102 
effect of manganese 

on, 93 
effect of phosphorus 
on, 92 



Wrought iron, effect of silicon on, 93 
sulphur on, 92 
expansion by heat, 102 
extension of, 103 
nails, weight of, 175 
properties of, 102 
strength of, 103 
tests for, 105 
welding, 102 

Wurtzilite, 46 



Yellow pine, blue sap in, 76 

bright sap in, 77 
pitch-streaks in, 76 
clear inspection, 85 
defects in rough stocky 

76,77 
dimension stock, 83 
dimensions of, flooring, 

ceiling, finishing, 83 
dressed timber, 82 
edge-grain, 77 
flat-grain, 78 
flooring, 82, 89 
lumber, inspection of, 83 
merchantable boaids and 
plank, 85 
flooring, 85 
inspection, 

84 
siding, 86 
plank, 83 

prime inspection, 84 
quarter-sawed, 89 
rift-sawed, 89 
rough edge, 84 

timber, 82 
scantling, 83 
stepping, 83 
square-edged inspection, 

84 
trade designations, 85 
Yield-point, 513 



Zinc chloride process for preserving 
timber, 66 
description of, 141 
expansion of, 141 
melting-point of, 141 
paint, 342 
precautions to be observed In 

the use of, 141 
properties of, 141 
shrinkage of, 148 
specific gravity of, 141 
strength of, 141 
weight of, 141 , 



ftrF 



191<»2 



SEP 19 1902 

1 COrY DEL. TO CAT DIV. 
^iP. 19 1802 



